title: M109 howitzer

text: Prototypes of the vehicle underwent government testing in preparation for a Low-Rate Initial Production (LRIP) decision. The testing included RAM, mission and ballistic hull and turret testing. The M109A7 was slated to begin LRIP by 2013. The U.S. Army planned on procuring a fleet of 580 sets of M109A7 howitzers and M992A3 Field Artillery Ammunition Support Vehicles (FAASVs).


title: M109 howitzer

text: In October 2013, the Defense Acquisition Board approved the decision to start M109A7 production. The FY 2014 budget called for $340.8 million in Paladin funding, which would be two dozen vehicle sets at $14.4 million per vehicle. The Army plans to buy 133 vehicles in 66 one-half vehicle sets starting in 2014, although one M109A7 howitzer and two supporting M992A3 ammunition carriers will be destroyed during tests. A Full-Rate Production (FRP) decision planned for February 2017. On 31 October 2013, BAE received a $668 million contract to begin LRIP of the M109A7. The first M109A6 and M992A2 vehicles were disassembled and reassembled to M109A7 and M992A3 standard as part of LRIP beginning in summer 2014. LRIP deliveries began in April 2015. The contract for FRP was signed in December 2017 with 48 vehicles slated for construction. The Army plans to upgrade 689 Paladins to A7-standard.


title: M109 howitzer

text: The Army is looking to increase the capabilities of the M109A7. By introducing the new XM1113 rocket-assisted projectile (RAP), it can reach from the current 39-caliber barrel, and a planned barrel extension to 58-caliber can increase its range to . An additional XM1113 improvement over the legacy RAP round is the replacement of the high explosive, TNT, with an insensitive munition that is less volatile and less prone to unplanned detonation. The Army is also working on an autoloader to increase sustained rate of fire to 6–10 rounds per minute. Another part of the effort is the use of a new supercharged propellant to fire the shells, which required redesigning the howitzer to handle higher pressures. These improvements are being developed under the Extended Range Cannon Artillery (ERCA) program, which upgrade the design so much it was re-designated the M1299; one battalion of vehicles is planned to begin a year-long operational assessment in 2023, and the autoloader is planned to be ready in 2025.


title: M109 howitzer

text: The M992 Field Artillery Ammunition Support Vehicle (FAASV) is built on the chassis of the M109. It replaced the M548. Unlike the M548, it is armored. This ammunition vehicle has no turret, but has a taller superstructure to store 93 rounds and an equivalent number of powders and primers.


title: M109 howitzer

text: This vehicle is fitted with a Halon fire suppression system and a weapons mount similar to that on the M109 turret, usually mounting a Mk 19 grenade launcher for local defense against infantry and light armored vehicles.


title: M109 howitzer

text: The vehicle also contains a 2-stroke diesel powered auxiliary power unit that can power all non-automotive energy requirements on the FAASV and on the M109.


title: M109 howitzer

text: The K66 was a planned ammunition support vehicle for the K55. As a follow-up to the K55 program, Samsung Aerospace Industries prepared for licensing a local variant of the M992 with modifications such as NBC protection and the increase of ammunition storage capacity to 110 rounds, 116 packs of powders, and 132 primers.


title: M109 howitzer

text: In 1987, Samsung Aerospace Industries completed against Daewoo Heavy Industries' ammunition support vehicle based on K200 APC. Daewoo Heavy Industries' vehicle was selected as the K66 but fell from the test evaluation. Eventually, the K66 project was cancelled in the mid-1990s as it expanded into a lawsuit.


title: M109 howitzer

text: The K56 ARV is a ammunition resupply vehicle based on the K55 platform. Unlike the K10 ARV, the K56 can resupply both K55A1 and K9 Thunder. It has a 45.7% (4,197 out of 9,191 total parts) compatibility with K55A1.


title: M109 howitzer

text: After 10 months of pilot experiment, the K56 program was authorized by DAPPC (Defense Acquisition Program Promotion Committee) on 16 February 2007. On 2 May, DAPPC allocated 16 billion KRW for research and development for 2008 to 2010, with planning to produce 520 vehicles between 2011 to 2020. On 26 June 2008, Samsung Techwin was selected as the main contractor for the project. Later, the development completion schedule was delayed to 2011 while the total production amount was increased to 700 vehicles with 1.3 trillion KRW between 2012 to 2021.


title: M109 howitzer

text: On 27 September 2010, the Board of Audit and Inspection claimed that the Army was biased during evaluation, demanding re-analyzing of the project due to inefficiency of the system. However, the Defense Acquisition Program Administration (DAPA) ignored the Board and continued with the project while the Army purposely delayed complying. On 14 June 2011, the Ministry of Defense once again ordered a reexamination of the resupply vehicle. Nevertheless, the DAPA requested a budget for the program instead, and the development was completed in October 2011. On 25 July 2013, the DAPA announced the 1st batch production of the K56 between 2013 to 2015 for 65 billion KRW.


title: M109 howitzer

text: In December 2015, Hanwha Techwin signed a contract with the DAPA for 2nd batch production. On 2 January 2018, Hanwha Land Systems announced 166.4 billion KRW contract with the DAPA for 3rd batch production and related products. On 30 June 2020, Hanwha Defense announced 380.3 billion KRW contract with the DAPA for 4th batch production. South Korea plans 5th batch production and achieving full operational capability by 2025. All K56s were delivered to the western front.


title: M109 howitzer

text: The US Army uses the Fire Support Combined Arms Tactical Trainer (FSCATT) in two versions for initial and sustainment training of the M109A6 and M109A5. The system uses an actual surplus turret and a simulated ammunition system.


title: M109 howitzer

text: The Dutch, Belgian, Thai, and Israeli Armies have various configurations of the Van Halteren Metaal M109 Howitzer Crew Trainer (HCT).


title: M109 howitzer

text: The US Army PEO STRI had a program called M109A7 Howitzer Crew Trainer (HCT). The plan was to procure 16 systems beginning in the 3rd Quarter of FY 20.


title: M109 howitzer

text: The U.S. Army sought to replace the M109 with the XM2001 Crusader, initially part of the Armored Systems Modernization program. The program was canceled in 2002 amid criticism that the program was not in line with the Army's long-term plans for lighter armored brigades. Funding was redirected to the Future Combat Systems Manned Ground Vehicles program, which produced the 18-ton XM1203 Non-Line-of-Sight Cannon as the program's lead effort. The Pentagon terminated the MGV program in 2009 due to concerns over its affordability. The U.S. Army's M1299 howitzer was planned to be completed in 2021 and will undergo operational assessment in 2023.


title: Chaos theory

text: Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to have completely random states of disorder and irregularities. Chaos theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnection, constant feedback loops, repetition, self-similarity, fractals, and self-organization. The butterfly effect, an underlying principle of chaos, describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state (meaning that there is sensitive dependence on initial conditions). A metaphor for this behavior is that a butterfly flapping its wings in Brazil can cause a tornado in Texas.


title: Chaos theory

text: Small differences in initial conditions, such as those due to errors in measurements or due to rounding errors in numerical computation, can yield widely diverging outcomes for such dynamical systems, rendering long-term prediction of their behavior impossible in general. This can happen even though these systems are deterministic, meaning that their future behavior follows a unique evolution and is fully determined by their initial conditions, with no random elements involved. In other words, the deterministic nature of these systems does not make them predictable. This behavior is known as deterministic chaos, or simply chaos. The theory was summarized by Edward Lorenz as:


title: Chaos theory

text: Chaotic behavior exists in many natural systems, including fluid flow, heartbeat irregularities, weather, and climate. It also occurs spontaneously in some systems with artificial components, such as the road traffic. This behavior can be studied through the analysis of a chaotic mathematical model, or through analytical techniques such as recurrence plots and Poincaré maps. Chaos theory has applications in a variety of disciplines, including meteorology, anthropology, sociology, environmental science, computer science, engineering, economics, ecology, and pandemic crisis management. The theory formed the basis for such fields of study as complex dynamical systems, edge of chaos theory, and self-assembly processes.


title: Chaos theory

text: Chaos theory concerns deterministic systems whose behavior can, in principle, be predicted. Chaotic systems are predictable for a while and then 'appear' to become random. The amount of time for which the behavior of a chaotic system can be effectively predicted depends on three things: how much uncertainty can be tolerated in the forecast, how accurately its current state can be measured, and a time scale depending on the dynamics of the system, called the Lyapunov time. Some examples of Lyapunov times are: chaotic electrical circuits, about 1 millisecond; weather systems, a few days (unproven); the inner solar system, 4 to 5 million years. In chaotic systems, the uncertainty in a forecast increases exponentially with elapsed time. Hence, mathematically, doubling the forecast time more than squares the proportional uncertainty in the forecast. This means, in practice, a meaningful prediction cannot be made over an interval of more than two or three times the Lyapunov time. When meaningful predictions cannot be made, the system appears random.


title: Chaos theory

text: Chaos theory is a method of qualitative and quantitative analysis to investigate the behavior of dynamic systems that cannot be explained and predicted by single data relationships, but must be explained and predicted by whole, continuous data relationships.


title: Chaos theory

text: In common usage, "chaos" means "a state of disorder". However, in chaos theory, the term is defined more precisely. Although no universally accepted mathematical definition of chaos exists, a commonly used definition, originally formulated by Robert L. Devaney, says that to classify a dynamical system as chaotic, it must have these properties:


title: Chaos theory

text: In some cases, the last two properties above have been shown to actually imply sensitivity to initial conditions. In the discrete-time case, this is true for all continuous maps on metric spaces. In these cases, while it is often the most practically significant property, "sensitivity to initial conditions" need not be stated in the definition.


title: Chaos theory

text: If attention is restricted to intervals, the second property implies the other two. An alternative and a generally weaker definition of chaos uses only the first two properties in the above list.


title: Chaos theory

text: Sensitivity to initial conditions means that each point in a chaotic system is arbitrarily closely approximated by other points that have significantly different future paths or trajectories. Thus, an arbitrarily small change or perturbation of the current trajectory may lead to significantly different future behavior.


title: Chaos theory

text: Sensitivity to initial conditions is popularly known as the "butterfly effect", so-called because of the title of a paper given by Edward Lorenz in 1972 to the American Association for the Advancement of Science in Washington, D.C., entitled "Predictability: Does the Flap of a Butterfly's Wings in Brazil set off a Tornado in Texas?". The flapping wing represents a small change in the initial condition of the system, which causes a chain of events that prevents the predictability of large-scale phenomena. Had the butterfly not flapped its wings, the trajectory of the overall system could have been vastly different.


title: Chaos theory

text: As suggested in Lorenz's book entitled ""The Essence of Chaos"", published in 1993, ""sensitive dependence can serve as an acceptable definition of chaos"". In the same book, Lorenz defined the butterfly effect as: ""The phenomenon that a small alteration in the state of a dynamical system will cause subsequent states to differ greatly from the states that would have followed without the alteration."" The above definition is consistent with the sensitive dependence of solutions on initial conditions (SDIC). An idealized skiing model was developed to illustrate the sensitivity of time-varying paths to initial positions. A predictability horizon can be determined before the onset of SDIC (i.e., prior to significant separations of initial nearby trajectories).


title: Chaos theory

text: A consequence of sensitivity to initial conditions is that if we start with a limited amount of information about the system (as is usually the case in practice), then beyond a certain time, the system would no longer be predictable. This is most prevalent in the case of weather, which is generally predictable only about a week ahead. This does not mean that one cannot assert anything about events far in the future—only that some restrictions on the system are present. For example, we know that the temperature of the surface of the earth will not naturally reach or fall below on earth (during the current geologic era), but we cannot predict exactly which day will have the hottest temperature of the year.


title: Chaos theory

text: In more mathematical terms, the Lyapunov exponent measures the sensitivity to initial conditions, in the form of rate of exponential divergence from the perturbed initial conditions. More specifically, given two starting trajectories in the phase space that are infinitesimally close, with initial separation formula_1, the two trajectories end up diverging at a rate given by


title: Chaos theory

text: where formula_3 is the time and formula_4 is the Lyapunov exponent. The rate of separation depends on the orientation of the initial separation vector, so a whole spectrum of Lyapunov exponents can exist. The number of Lyapunov exponents is equal to the number of dimensions of the phase space, though it is common to just refer to the largest one. For example, the maximal Lyapunov exponent (MLE) is most often used, because it determines the overall predictability of the system. A positive MLE is usually taken as an indication that the system is chaotic.


title: Chaos theory

text: In addition to the above property, other properties related to sensitivity of initial conditions also exist. These include, for example, measure-theoretical mixing (as discussed in ergodic theory) and properties of a K-system.


title: Chaos theory

text: A chaotic system may have sequences of values for the evolving variable that exactly repeat themselves, giving periodic behavior starting from any point in that sequence. However, such periodic sequences are repelling rather than attracting, meaning that if the evolving variable is outside the sequence, however close, it will not enter the sequence and in fact, will diverge from it. Thus for almost all initial conditions, the variable evolves chaotically with non-periodic behavior.


title: Chaos theory

text: Topological mixing (or the weaker condition of topological transitivity) means that the system evolves over time so that any given region or open set of its phase space eventually overlaps with any other given region. This mathematical concept of "mixing" corresponds to the standard intuition, and the mixing of colored dyes or fluids is an example of a chaotic system.


title: Chaos theory

text: Topological mixing is often omitted from popular accounts of chaos, which equate chaos with only sensitivity to initial conditions. However, sensitive dependence on initial conditions alone does not give chaos. For example, consider the simple dynamical system produced by repeatedly doubling an initial value. This system has sensitive dependence on initial conditions everywhere, since any pair of nearby points eventually becomes widely separated. However, this example has no topological mixing, and therefore has no chaos. Indeed, it has extremely simple behavior: all points except 0 tend to positive or negative infinity.


title: Chaos theory

text: A map formula_5 is said to be topologically transitive if for any pair of non-empty open sets formula_6, there exists formula_7 such that formula_8. Topological transitivity is a weaker version of topological mixing. Intuitively, if a map is topologically transitive then given a point "x" and a region "V", there exists a point "y" near "x" whose orbit passes through "V". This implies that it is impossible to decompose the system into two open sets.


title: Chaos theory

text: An important related theorem is the Birkhoff Transitivity Theorem. It is easy to see that the existence of a dense orbit implies topological transitivity. The Birkhoff Transitivity Theorem states that if "X" is a second countable, complete metric space, then topological transitivity implies the existence of a dense set of points in "X" that have dense orbits.


title: Chaos theory

text: For a chaotic system to have dense periodic orbits means that every point in the space is approached arbitrarily closely by periodic orbits. The one-dimensional logistic map defined by "x" → 4 "x" (1 – "x") is one of the simplest systems with density of periodic orbits. For example, formula_9 → formula_10 → formula_9 (or approximately 0.3454915 → 0.9045085 → 0.3454915) is an (unstable) orbit of period 2, and similar orbits exist for periods 4, 8, 16, etc. (indeed, for all the periods specified by Sharkovskii's theorem).


title: Chaos theory

text: Sharkovskii's theorem is the basis of the Li and Yorke (1975) proof that any continuous one-dimensional system that exhibits a regular cycle of period three will also display regular cycles of every other length, as well as completely chaotic orbits.


title: Chaos theory

text: Some dynamical systems, like the one-dimensional logistic map defined by "x" → 4 "x" (1 – "x"), are chaotic everywhere, but in many cases chaotic behavior is found only in a subset of phase space. The cases of most interest arise when the chaotic behavior takes place on an attractor, since then a large set of initial conditions leads to orbits that converge to this chaotic region.


title: Chaos theory

text: An easy way to visualize a chaotic attractor is to start with a point in the basin of attraction of the attractor, and then simply plot its subsequent orbit. Because of the topological transitivity condition, this is likely to produce a picture of the entire final attractor, and indeed both orbits shown in the figure on the right give a picture of the general shape of the Lorenz attractor. This attractor results from a simple three-dimensional model of the Lorenz weather system. The Lorenz attractor is perhaps one of the best-known chaotic system diagrams, probably because it is not only one of the first, but it is also one of the most complex, and as such gives rise to a very interesting pattern that, with a little imagination, looks like the wings of a butterfly.


title: Chaos theory

text: Unlike fixed-point attractors and limit cycles, the attractors that arise from chaotic systems, known as strange attractors, have great detail and complexity. Strange attractors occur in both continuous dynamical systems (such as the Lorenz system) and in some discrete systems (such as the Hénon map). Other discrete dynamical systems have a repelling structure called a Julia set, which forms at the boundary between basins of attraction of fixed points. Julia sets can be thought of as strange repellers. Both strange attractors and Julia sets typically have a fractal structure, and the fractal dimension can be calculated for them.


title: Chaos theory

text: In contrast to single type chaotic solutions, recent studies using Lorenz models have emphasized the importance of considering various types of solutions. For example, coexisting chaotic and non-chaotic may appear within the same model (e.g., the double pendulum system) using the same modeling configurations but different initial conditions. The findings of attractor coexistence, obtained from classical and generalized Lorenz models, suggested a revised view that “the entirety of weather possesses a dual nature of chaos and order with distinct predictability”, in contrast to the conventional view of “weather is chaotic”.


title: Chaos theory

text: Discrete chaotic systems, such as the logistic map, can exhibit strange attractors whatever their dimensionality. Universality of one-dimensional maps with parabolic maxima and Feigenbaum constants formula_12,formula_13 is well visible with map proposed as a toy


title: Chaos theory

text: where formula_15 stands for electric field amplitude, formula_16 is laser gain as bifurcation parameter. The gradual increase of formula_16 at interval formula_18 changes dynamics from regular to chaotic one with qualitatively the same bifurcation diagram as those for logistic map.


title: Chaos theory

text: In contrast, for continuous dynamical systems, the Poincaré–Bendixson theorem shows that a strange attractor can only arise in three or more dimensions. Finite-dimensional linear systems are never chaotic; for a dynamical system to display chaotic behavior, it must be either nonlinear or infinite-dimensional.


title: Chaos theory

text: The Poincaré–Bendixson theorem states that a two-dimensional differential equation has very regular behavior. The Lorenz attractor discussed below is generated by a system of three differential equations such as:


title: Chaos theory

text: where formula_15, formula_21, and formula_22 make up the system state, formula_3 is time, and formula_24, formula_25, formula_26 are the system parameters. Five of the terms on the right hand side are linear, while two are quadratic; a total of seven terms. Another well-known chaotic attractor is generated by the Rössler equations, which have only one nonlinear term out of seven. Sprott found a three-dimensional system with just five terms, that had only one nonlinear term, which exhibits chaos for certain parameter values. Zhang and Heidel showed that, at least for dissipative and conservative quadratic systems, three-dimensional quadratic systems with only three or four terms on the right-hand side cannot exhibit chaotic behavior. The reason is, simply put, that solutions to such systems are asymptotic to a two-dimensional surface and therefore solutions are well behaved.


title: Chaos theory

text: While the Poincaré–Bendixson theorem shows that a continuous dynamical system on the Euclidean plane cannot be chaotic, two-dimensional continuous systems with non-Euclidean geometry can exhibit chaotic behavior. Perhaps surprisingly, chaos may occur also in linear systems, provided they are infinite dimensional. A theory of linear chaos is being developed in a branch of mathematical analysis known as functional analysis.


title: Chaos theory

text: The above elegant set of three ordinary differential equations has been referred to as the three-dimensional Lorenz model. Since 1963, higher-dimensional Lorenz models have been developed in numerous studies for examining the impact of an increased degree of nonlinearity, as well as its collective effect with heating and dissipations, on solution stability.


title: Chaos theory

text: The straightforward generalization of coupled discrete maps is based upon convolution integral which mediates interaction between spatially distributed maps:


title: Chaos theory

text: formula_29 might be logistic map alike formula_30 or complex map. For examples of complex maps the Julia set formula_31 or Ikeda map


title: Chaos theory

text: formula_32 may serve. When wave propagation problems at distance formula_33 with wavelength formula_34 are considered the kernel formula_35 may have a form of Green function for Schrödinger equation:.


title: Chaos theory

text: In physics, jerk is the third derivative of position, with respect to time. As such, differential equations of the form


title: Chaos theory

text: are sometimes called "jerk equations". It has been shown that a jerk equation, which is equivalent to a system of three first order, ordinary, non-linear differential equations, is in a certain sense the minimal setting for solutions showing chaotic behavior. This motivates mathematical interest in jerk systems. Systems involving a fourth or higher derivative are called accordingly hyperjerk systems.


title: Chaos theory

text: A jerk system's behavior is described by a jerk equation, and for certain jerk equations, simple electronic circuits can model solutions. These circuits are known as jerk circuits.


title: Chaos theory

text: One of the most interesting properties of jerk circuits is the possibility of chaotic behavior. In fact, certain well-known chaotic systems, such as the Lorenz attractor and the Rössler map, are conventionally described as a system of three first-order differential equations that can combine into a single (although rather complicated) jerk equation. Another example of a jerk equation with nonlinearity in the magnitude of formula_15 is:


title: Chaos theory

text: Here, "A" is an adjustable parameter. This equation has a chaotic solution for "A"=3/5 and can be implemented with the following jerk circuit; the required nonlinearity is brought about by the two diodes:


title: Chaos theory

text: In the above circuit, all resistors are of equal value, except formula_40, and all capacitors are of equal size. The dominant frequency is formula_41. The output of op amp 0 will correspond to the x variable, the output of 1 corresponds to the first derivative of x and the output of 2 corresponds to the second derivative.


title: Chaos theory

text: See also the well-known Chua's circuit, one basis for chaotic true random number generators. The ease of construction of the circuit has made it a ubiquitous real-world example of a chaotic system.


title: Chaos theory

text: Under the right conditions, chaos spontaneously evolves into a lockstep pattern. In the Kuramoto model, four conditions suffice to produce synchronization in a chaotic system.


title: Chaos theory

text: Examples include the coupled oscillation of Christiaan Huygens' pendulums, fireflies, neurons, the London Millennium Bridge resonance, and large arrays of Josephson junctions.


title: Chaos theory

text: An early proponent of chaos theory was Henri Poincaré. In the 1880s, while studying the three-body problem, he found that there can be orbits that are nonperiodic, and yet not forever increasing nor approaching a fixed point. In 1898, Jacques Hadamard published an influential study of the chaotic motion of a free particle gliding frictionlessly on a surface of constant negative curvature, called "Hadamard's billiards". Hadamard was able to show that all trajectories are unstable, in that all particle trajectories diverge exponentially from one another, with a positive Lyapunov exponent.


title: Chaos theory

text: Chaos theory began in the field of ergodic theory. Later studies, also on the topic of nonlinear differential equations, were carried out by George David Birkhoff, Andrey Nikolaevich Kolmogorov, Mary Lucy Cartwright and John Edensor Littlewood, and Stephen Smale. Except for Smale, these studies were all directly inspired by physics: the three-body problem in the case of Birkhoff, turbulence and astronomical problems in the case of Kolmogorov, and radio engineering in the case of Cartwright and Littlewood. Although chaotic planetary motion had not been observed, experimentalists had encountered turbulence in fluid motion and nonperiodic oscillation in radio circuits without the benefit of a theory to explain what they were seeing.


title: Chaos theory

text: Despite initial insights in the first half of the twentieth century, chaos theory became formalized as such only after mid-century, when it first became evident to some scientists that linear theory, the prevailing system theory at that time, simply could not explain the observed behavior of certain experiments like that of the logistic map. What had been attributed to measure imprecision and simple "noise" was considered by chaos theorists as a full component of the studied systems.


title: Chaos theory

text: The main catalyst for the development of chaos theory was the electronic computer. Much of the mathematics of chaos theory involves the repeated iteration of simple mathematical formulas, which would be impractical to do by hand. Electronic computers made these repeated calculations practical, while figures and images made it possible to visualize these systems. As a graduate student in Chihiro Hayashi's laboratory at Kyoto University, Yoshisuke Ueda was experimenting with analog computers and noticed, on November 27, 1961, what he called "randomly transitional phenomena". Yet his advisor did not agree with his conclusions at the time, and did not allow him to report his findings until 1970.


title: Chaos theory

text: Edward Lorenz was an early pioneer of the theory. His interest in chaos came about accidentally through his work on weather prediction in 1961. Lorenz and his collaborator Ellen Fetter were using a simple digital computer, a Royal McBee LGP-30, to run weather simulations. They wanted to see a sequence of data again, and to save time they started the simulation in the middle of its course. They did this by entering a printout of the data that corresponded to conditions in the middle of the original simulation. To their surprise, the weather the machine began to predict was completely different from the previous calculation. They tracked this down to the computer printout. The computer worked with 6-digit precision, but the printout rounded variables off to a 3-digit number, so a value like 0.506127 printed as 0.506. This difference is tiny, and the consensus at the time would have been that it should have no practical effect. However, Lorenz discovered that small changes in initial conditions produced large changes in long-term outcome. Lorenz's discovery, which gave its name to Lorenz attractors, showed that even detailed atmospheric modeling cannot, in general, make precise long-term weather predictions.


title: Chaos theory

text: In 1963, Benoit Mandelbrot found recurring patterns at every scale in data on cotton prices. Beforehand he had studied information theory and concluded noise was patterned like a Cantor set: on any scale the proportion of noise-containing periods to error-free periods was a constant – thus errors were inevitable and must be planned for by incorporating redundancy. Mandelbrot described both the "Noah effect" (in which sudden discontinuous changes can occur) and the "Joseph effect" (in which persistence of a value can occur for a while, yet suddenly change afterwards). This challenged the idea that changes in price were normally distributed. In 1967, he published "How long is the coast of Britain? Statistical self-similarity and fractional dimension", showing that a coastline's length varies with the scale of the measuring instrument, resembles itself at all scales, and is infinite in length for an infinitesimally small measuring device. Arguing that a ball of twine appears as a point when viewed from far away (0-dimensional), a ball when viewed from fairly near (3-dimensional), or a curved strand (1-dimensional), he argued that the dimensions of an object are relative to the observer and may be fractional. An object whose irregularity is constant over different scales ("self-similarity") is a fractal (examples include the Menger sponge, the Sierpiński gasket, and the Koch curve or "snowflake", which is infinitely long yet encloses a finite space and has a fractal dimension of circa 1.2619). In 1982, Mandelbrot published "The Fractal Geometry of Nature", which became a classic of chaos theory.


title: Chaos theory

text: In December 1977, the New York Academy of Sciences organized the first symposium on chaos, attended by David Ruelle, Robert May, James A. Yorke (coiner of the term "chaos" as used in mathematics), Robert Shaw, and the meteorologist Edward Lorenz. The following year Pierre Coullet and Charles Tresser published "Itérations d'endomorphismes et groupe de renormalisation", and Mitchell Feigenbaum's article "Quantitative Universality for a Class of Nonlinear Transformations" finally appeared in a journal, after 3 years of referee rejections. Thus Feigenbaum (1975) and Coullet & Tresser (1978) discovered the universality in chaos, permitting the application of chaos theory to many different phenomena.


title: Chaos theory

text: In 1979, Albert J. Libchaber, during a symposium organized in Aspen by Pierre Hohenberg, presented his experimental observation of the bifurcation cascade that leads to chaos and turbulence in Rayleigh–Bénard convection systems. He was awarded the Wolf Prize in Physics in 1986 along with Mitchell J. Feigenbaum for their inspiring achievements.


title: Chaos theory

text: In 1986, the New York Academy of Sciences co-organized with the National Institute of Mental Health and the Office of Naval Research the first important conference on chaos in biology and medicine. There, Bernardo Huberman presented a mathematical model of the eye tracking dysfunction among people with schizophrenia. This led to a renewal of physiology in the 1980s through the application of chaos theory, for example, in the study of pathological cardiac cycles.


title: Chaos theory

text: In 1987, Per Bak, Chao Tang and Kurt Wiesenfeld published a paper in "Physical Review Letters" describing for the first time self-organized criticality (SOC), considered one of the mechanisms by which complexity arises in nature.


title: Chaos theory

text: Alongside largely lab-based approaches such as the Bak–Tang–Wiesenfeld sandpile, many other investigations have focused on large-scale natural or social systems that are known (or suspected) to display scale-invariant behavior. Although these approaches were not always welcomed (at least initially) by specialists in the subjects examined, SOC has nevertheless become established as a strong candidate for explaining a number of natural phenomena, including earthquakes, (which, long before SOC was discovered, were known as a source of scale-invariant behavior such as the Gutenberg–Richter law describing the statistical distribution of earthquake sizes, and the Omori law describing the frequency of aftershocks), solar flares, fluctuations in economic systems such as financial markets (references to SOC are common in econophysics), landscape formation, forest fires, landslides, epidemics, and biological evolution (where SOC has been invoked, for example, as the dynamical mechanism behind the theory of "punctuated equilibria" put forward by Niles Eldredge and Stephen Jay Gould). Given the implications of a scale-free distribution of event sizes, some researchers have suggested that another phenomenon that should be considered an example of SOC is the occurrence of wars. These investigations of SOC have included both attempts at modelling (either developing new models or adapting existing ones to the specifics of a given natural system), and extensive data analysis to determine the existence and/or characteristics of natural scaling laws.


title: Chaos theory

text: In the same year, James Gleick published "", which became a best-seller and introduced the general principles of chaos theory as well as its history to the broad public. Initially the domain of a few, isolated individuals, chaos theory progressively emerged as a transdisciplinary and institutional discipline, mainly under the name of nonlinear systems analysis. Alluding to Thomas Kuhn's concept of a paradigm shift exposed in "The Structure of Scientific Revolutions" (1962), many "chaologists" (as some described themselves) claimed that this new theory was an example of such a shift, a thesis upheld by Gleick.


title: Chaos theory

text: The availability of cheaper, more powerful computers broadens the applicability of chaos theory. Currently, chaos theory remains an active area of research, involving many different disciplines such as mathematics, topology, physics, social systems, population modeling, biology, meteorology, astrophysics, information theory, computational neuroscience, pandemic crisis management, etc.


title: Chaos theory

text: Although chaos theory was born from observing weather patterns, it has become applicable to a variety of other situations. Some areas benefiting from chaos theory today are geology, mathematics, biology, computer science, economics, engineering, finance, meteorology, philosophy, anthropology, physics, politics, population dynamics, and robotics. A few categories are listed below with examples, but this is by no means a comprehensive list as new applications are appearing.


title: Chaos theory

text: Chaos theory has been used for many years in cryptography. In the past few decades, chaos and nonlinear dynamics have been used in the design of hundreds of cryptographic primitives. These algorithms include image encryption algorithms, hash functions, secure pseudo-random number generators, stream ciphers, watermarking, and steganography. The majority of these algorithms are based on uni-modal chaotic maps and a big portion of these algorithms use the control parameters and the initial condition of the chaotic maps as their keys. From a wider perspective, without loss of generality, the similarities between the chaotic maps and the cryptographic systems is the main motivation for the design of chaos based cryptographic algorithms. One type of encryption, secret key or symmetric key, relies on diffusion and confusion, which is modeled well by chaos theory. Another type of computing, DNA computing, when paired with chaos theory, offers a way to encrypt images and other information. Many of the DNA-Chaos cryptographic algorithms are proven to be either not secure, or the technique applied is suggested to be not efficient.


title: Chaos theory

text: Robotics is another area that has recently benefited from chaos theory. Instead of robots acting in a trial-and-error type of refinement to interact with their environment, chaos theory has been used to build a predictive model.


title: Chaos theory

text: For over a hundred years, biologists have been keeping track of populations of different species with population models. Most models are continuous, but recently scientists have been able to implement chaotic models in certain populations. For example, a study on models of Canadian lynx showed there was chaotic behavior in the population growth. Chaos can also be found in ecological systems, such as hydrology. While a chaotic model for hydrology has its shortcomings, there is still much to learn from looking at the data through the lens of chaos theory. Another biological application is found in cardiotocography. Fetal surveillance is a delicate balance of obtaining accurate information while being as noninvasive as possible. Better models of warning signs of fetal hypoxia can be obtained through chaotic modeling.


title: Chaos theory

text: It is possible that economic models can also be improved through an application of chaos theory, but predicting the health of an economic system and what factors influence it most is an extremely complex task. Economic and financial systems are fundamentally different from those in the classical natural sciences since the former are inherently stochastic in nature, as they result from the interactions of people, and thus pure deterministic models are unlikely to provide accurate representations of the data. The empirical literature that tests for chaos in economics and finance presents very mixed results, in part due to confusion between specific tests for chaos and more general tests for non-linear relationships.


title: Chaos theory

text: Chaos could be found in economics by the means of recurrence quantification analysis. In fact, Orlando et al. by the means of the so-called recurrence quantification correlation index were able detect hidden changes in time series. Then, the same technique was employed to detect transitions from laminar (regular) to turbulent (chaotic) phases as well as differences between macroeconomic variables and highlight hidden features of economic dynamics. Finally, chaos could help in modeling how economy operate as well as in embedding shocks due to external events such as COVID-19.


title: Chaos theory

text: In chemistry, predicting gas solubility is essential to manufacturing polymers, but models using particle swarm optimization (PSO) tend to converge to the wrong points. An improved version of PSO has been created by introducing chaos, which keeps the simulations from getting stuck. In celestial mechanics, especially when observing asteroids, applying chaos theory leads to better predictions about when these objects will approach Earth and other planets. Four of the five moons of Pluto rotate chaotically. In quantum physics and electrical engineering, the study of large arrays of Josephson junctions benefitted greatly from chaos theory. Closer to home, coal mines have always been dangerous places where frequent natural gas leaks cause many deaths. Until recently, there was no reliable way to predict when they would occur. But these gas leaks have chaotic tendencies that, when properly modeled, can be predicted fairly accurately.


title: Chaos theory

text: Chaos theory can be applied outside of the natural sciences, but historically nearly all such studies have suffered from lack of reproducibility; poor external validity; and/or inattention to cross-validation, resulting in poor predictive accuracy (if out-of-sample prediction has even been attempted). Glass and Mandell and Selz have found that no EEG study has as yet indicated the presence of strange attractors or other signs of chaotic behavior.


title: Chaos theory

text: Researchers have continued to apply chaos theory to psychology. For example, in modeling group behavior in which heterogeneous members may behave as if sharing to different degrees what in Wilfred Bion's theory is a basic assumption, researchers have found that the group dynamic is the result of the individual dynamics of the members: each individual reproduces the group dynamics in a different scale, and the chaotic behavior of the group is reflected in each member.


title: Chaos theory

text: Redington and Reidbord (1992) attempted to demonstrate that the human heart could display chaotic traits. They monitored the changes in between-heartbeat intervals for a single psychotherapy patient as she moved through periods of varying emotional intensity during a therapy session. Results were admittedly inconclusive. Not only were there ambiguities in the various plots the authors produced to purportedly show evidence of chaotic dynamics (spectral analysis, phase trajectory, and autocorrelation plots), but also when they attempted to compute a Lyapunov exponent as more definitive confirmation of chaotic behavior, the authors found they could not reliably do so.


title: Chaos theory

text: In their 1995 paper, Metcalf and Allen maintained that they uncovered in animal behavior a pattern of period doubling leading to chaos. The authors examined a well-known response called schedule-induced polydipsia, by which an animal deprived of food for certain lengths of time will drink unusual amounts of water when the food is at last presented. The control parameter (r) operating here was the length of the interval between feedings, once resumed. The authors were careful to test a large number of animals and to include many replications, and they designed their experiment so as to rule out the likelihood that changes in response patterns were caused by different starting places for r.


title: Chaos theory

text: Time series and first delay plots provide the best support for the claims made, showing a fairly clear march from periodicity to irregularity as the feeding times were increased. The various phase trajectory plots and spectral analyses, on the other hand, do not match up well enough with the other graphs or with the overall theory to lead inexorably to a chaotic diagnosis. For example, the phase trajectories do not show a definite progression towards greater and greater complexity (and away from periodicity); the process seems quite muddied. Also, where Metcalf and Allen saw periods of two and six in their spectral plots, there is room for alternative interpretations. All of this ambiguity necessitate some serpentine, post-hoc explanation to show that results fit a chaotic model.


title: Chaos theory

text: By adapting a model of career counseling to include a chaotic interpretation of the relationship between employees and the job market, Amundson and Bright found that better suggestions can be made to people struggling with career decisions. Modern organizations are increasingly seen as open complex adaptive systems with fundamental natural nonlinear structures, subject to internal and external forces that may contribute chaos. For instance, team building and group development is increasingly being researched as an inherently unpredictable system, as the uncertainty of different individuals meeting for the first time makes the trajectory of the team unknowable.


title: Chaos theory

text: Some say the chaos metaphor—used in verbal theories—grounded on mathematical models and psychological aspects of human behavior


title: Chaos theory

text: provides helpful insights to describing the complexity of small work groups, that go beyond the metaphor itself.


title: Chaos theory

text: Traffic forecasting may benefit from applications of chaos theory. Better predictions of when a congestion will occur would allow measures to be taken to disperse it before it would have occurred. Combining chaos theory principles with a few other methods has led to a more accurate short-term prediction model (see the plot of the BML traffic model at right).


title: Chaos theory

text: Chaos theory has been applied to environmental water cycle data (also hydrological data), such as rainfall and streamflow. These studies have yielded controversial results, because the methods for detecting a chaotic signature are often relatively subjective. Early studies tended to "succeed" in finding chaos, whereas subsequent studies and meta-analyses called those studies into question and provided explanations for why these datasets are not likely to have low-dimension chaotic dynamics.


title: Aleksandr Dugin

text: Aleksandr Gelyevich Dugin (; born 7 January 1962) is a Russian political philosopher, analyst, and strategist, who has been widely characterized as a fascist.


title: Aleksandr Dugin

text: Born into a military intelligence family, Dugin was an anti-communist dissident during the 1980s. Following the dissolution of the Soviet Union, Dugin co-founded the National Bolshevik Party with Eduard Limonov, a party which espoused National Bolshevism, which he later left. In 1997, he published "Foundations of Geopolitics", in which he outlined his worldview, calling for Russia to rebuild its influence through alliances and conquest, and to challenge the rival Atlanticist "empire" led by the United States. Dugin continued to further develop his ideology of neo-Eurasianism, founding the Eurasia Party in 2002 and writing further books including "The Fourth Political Theory" (2009).


title: Aleksandr Dugin

text: Dugin also served as an advisor to the Chairman of the State Duma Gennadiy Seleznyov (Communist Party) and as an advisor to the Chairman of the State Duma Sergey Naryshkin (United Russia). He was the head of the Department of Sociology of International Relations at Moscow State University from 2009 to 2014, losing the position due to backlash over comments regarding clashes in Ukraine. Dugin also briefly served as chief editor of the pro-Kremlin Orthodox channel Tsargrad TV when it launched in 2015.


title: Aleksandr Dugin

text: His influence on the Russian government and on president Vladimir Putin is disputed. He has no official ties to the Kremlin, but is often referred to in the media as "Putin's brain", though others say his influence is exaggerated.


title: Aleksandr Dugin

text: Dugin was born in Moscow, into the family of a colonel-general in the Soviet military intelligence and candidate of law, Geliy Alexandrovich Dugin, and his wife Galina, a doctor and candidate of medicine. His father left the family when he was three, but ensured that they had a good standard of living, and helped Dugin out of trouble with the authorities on occasion. He was transferred to the customs service due to his son's behaviour in 1983.


title: Aleksandr Dugin

text: In 1979, Aleksandr entered the Moscow Aviation Institute. He was expelled without a degree either because of low academic achievement, dissident activities or both. Afterwards, he began working as a street cleaner. He used a forged reader's card to access the Lenin Library and continue studying. However, other sources claim he instead started working in a KGB archive, where he had access to banned literature on Masonry, fascism and paganism.


title: Aleksandr Dugin

text: In 1980, Dugin joined the "", an avant-garde dissident group which dabbled in Satanism, esoteric Nazism and other forms of the occult. In the group, he was known for his embrace of Nazism which he attributes to a rebellion against his Soviet raising, as opposed to genuine sympathy for Hitler. He adopted an alter ego with the name of "Hans Sievers", a reference to Wolfram Sievers, a Nazi researcher of the paranormal.


title: Aleksandr Dugin

text: Studying by himself, he learned to speak Italian, German, French, English and Spanish. He was influenced by René Guénon and by the Traditionalist School. In the V. I. Lenin State Library he discovered the writings of Julius Evola, whose book "Pagan Imperialism" he translated into Russian.


title: Aleksandr Dugin

text: In the 1980s, Dugin was a dissident and an anti-communist. Dugin worked as a journalist before becoming involved in politics just before the fall of communism. In 1988, he and his friend Geydar Dzhemal joined the ultranationalist and anti-Semitic group Pamyat (Memory), which would later give rise to Russian fascism. For a brief period at the beginning of the 1990s he was close to Gennady Zyuganov, leader of the newly formed Communist Party of the Russian Federation, and probably had a role in formulating its nationalist communist ideology. In 1993 he co-founded, together with Eduard Limonov, the National Bolshevik Party, whose nationalistic interpretation of Bolshevism was based on the ideas of Ernst Niekisch. He left the party in 1998 following disputes with Limonov.


title: Aleksandr Dugin

text: Dugin published "Foundations of Geopolitics" in 1997. The book was published in multiple editions, and is used in university courses on geopolitics, reportedly including the Academy of the General Staff of the Russian military. It alarmed political scientists in the US, and is sometimes referenced by them as being "Russia's Manifest Destiny". In 1997, his article, "Fascism – Borderless and Red", described "national capitalism" as pre-empting the development of a "genuine, true, radically revolutionary and consistent, fascist fascism" in Russia. He believes that it was "by no means the racist and chauvinist aspects of National Socialism that determined the nature of its ideology. The excesses of this ideology in Germany are a matter exclusively of the Germans... while Russian fascism is a combination of natural national conservatism with a passionate desire for true changes." The "Waffen-SS and especially the scientific sector of this organization, Ahnenerbe," was "an intellectual oasis in the framework of the National Socialist regime", according to him.


title: Aleksandr Dugin

text: Dugin soon began publishing his own journal entitled "Elementy", which initially began by praising Franco-Belgian Jean-François Thiriart, belatedly a supporter of a "Euro-Soviet empire which would stretch from Dublin to Vladivostok and would also need to expand to the south, since it require(s) a port on the Indian Ocean." Consistently glorifying both Tsarist and Stalinist Russia, "Elementy" also indicated his admiration for Julius Evola. Dugin also collaborated with the weekly journal "Den" (The Day), previously directed by Alexander Prokhanov.


title: Aleksandr Dugin

text: Dugin disapproves of liberalism and the West, particularly US hegemony. He asserts: "We are on the side of Stalin and the Soviet Union". He describes himself as being a conservative: "We, conservatives, want a strong, solid state, want order and healthy family, positive values, the reinforcing of the importance of religion and the Church in society". He adds: "We want patriotic radio, TV, patriotic experts, patriotic clubs. We want the media that expresses national interests".


title: Aleksandr Dugin

text: According to political scientist Marlène Laruelle, the thinking of Dugin, main manufacturer of a fascism "à-la-russe", could be described as a series of concentric circles, with far-right ideologies underpinned by different political and philosophical traditions (Esoteric Nazism, Traditionalism/Perennialism, the German Conservative Revolution and the European New Right) at its backbone.


title: Aleksandr Dugin

text: Dugin adapts Martin Heidegger's thought of "Dasein" (Existence) and transforms it into a geo–philosophical concept. According to Dugin, the forces of liberal and capitalist Western civilization represent what the ancient Greeks called "ὕβρις" (hubris), "the essential form of titanism" (the anti-ideal form), which opposes Heaven ("the ideal form—in terms of space, time, being"). In other words, the West would summarize "the revolt of the Earth against Heaven". To what he calls the West's "atomizing" universalism, Dugin contrasts an apophatic universalism, expressed in the political idea of "empire". Values of democracy, human rights and individualism are considered by him not to be universal but uniquely Western.


title: Aleksandr Dugin

text: In 2019, Dugin engaged in a debate with French intellectual Bernard-Henri Lévy on the theme of what has been called "the crisis of capitalism" and the insurrection of nationalist populisms.


title: Aleksandr Dugin

text: Dugin has theorized the foundation of a "Euro-Asian empire" capable of fighting the US-led Western world. In this regard, he was the organizer and the first leader of the ultranationalist National Bolshevik Party from 1993 to 1998 (along with Eduard Limonov) and, subsequently, of the National Bolshevik Front and of the Eurasia Party, which then became a non-governmental association. Dugin's Eurasitic ideology therefore aims at the unification of all Russian-speaking peoples in a single country. His views have been characterised as Fascist by some critics.


title: Aleksandr Dugin

text: In the early 1990s, Dugin's work at the National Bolshevik Front included research into the roots of national movements and the activities of supporting esoteric groups in the first half of the 20th century. Partnering with Christian Bouchet, a then-member of the French Ordo Templi Orientis, and building on Nationalist and migratory-integrative interest groups in Asia and Europe, they contribute in bringing international politics closer to Russia's Eurasian geopolitical concept.


title: Aleksandr Dugin

text: Dugin spent two years studying the geopolitical, semiotic and esoteric theories of the controversial German thinker Herman Wirth (1885–1981), one of the founders of the German Ahnenerbe. This resulted in the book "Hyperborean Theory" (1993), in which Dugin largely endorsed Wirth's ideas as a possible foundation for his Eurasianism. Apparently, this is "one of the most extensive summaries and treatments of Wirth in any language". According to the Moldovan anthropologist Leonid Mosionjnik, Wirth's overtly wild ideas fitted perfectly well in the ideological void after the demise of communism, liberalism and democracy. Dugin also promoted Wirth's claim to have written a book on the history of the Jewish People and the Old Testament, the so-called "Palestinabuch", which could have changed the world had it not been stolen.


title: Aleksandr Dugin

text: Dugin's ideas, particularly those on "a Turkic–Slavic alliance in the Eurasian sphere", have begun to receive attention among certain nationalistic circles in Turkey, most notably among alleged members of the Ergenekon network, which is the subject of a high-profile trial (on charges of conspiracy). Dugin's Eurasianist ideology has also been linked to his adherence to the doctrines of the Traditionalist School. (Dugin's Traditionalist beliefs are the subject of a book length study by J. Heiser, "The American Empire Should Be Destroyed—Aleksandr Dugin and the Perils of Immanentized Eschatology.") Dugin also advocates for a Russo-Arab alliance.


title: Aleksandr Dugin

text: The reborn Russia, according to Dugin's concept, is said by Charles Clover of the "Financial Times" to be a slightly remade version of the Soviet Union with echoes of "Nineteen Eighty-Four" by George Orwell, where Eurasia was one of three continent-sized super states including Eastasia and Oceania as the other two and was participating in endless war between them. In the Eurasian public discourse sphere, the totalitarian communist policy deployed in over three decades of works by various international groups that are part of the movement, is "a version of reintegration of the post-Soviet space into a 'Eurasian' sphere of influence for Russia". The North American program "works with a wide range of partners from all sectors of civil society" and "is advanced through grant making, advocacy and research, regional initiatives, and close engagement".


title: Aleksandr Dugin

text: The Kremlin invited Dugin to speak at its Anti-Orange Rally in Moscow in February 2012. There, Dugin addressed tens of thousands with this message:


title: Aleksandr Dugin

text: Dugin was baptized at the age of six in the Russian Orthodox church of Michurinsk by his great-grandmother Elena Mikhailovna Kargaltseva. Since 1999, he formally embraced a branch of the Old Believers, a Russian religious movement which rejected the 1652–1666 reforms of the official Russian Orthodox Church. Dugin's Eurasian philosophy owes much to Traditional Integralism and "Nouvelle Droite" movements, and as such it resonates with Neopaganism, a category which in this context means the movement of Slavic Native Faith (Rodnovery), especially in the forms of Anastasianism and Ynglism.


title: Aleksandr Dugin

text: Dugin's Eurasianism is often cited as belonging to the same spectrum of these movements, as well as also having influences from Hermetic, Gnostic and Eastern traditions. He calls to rely upon "Eastern theology and mystical currents" for the development of the Fourth Political Theory.


title: Aleksandr Dugin

text: According to Marlene Laruelle, Dugin's adherence to the Old Believers allows him to stand between Paganism and Orthodox Christianity without formally adopting either of them. His choice is not paradoxical, since, according to him—in the wake of René Guénon—Russian Orthodoxy and especially the Old Believers have preserved an esoteric and initiatory character which was utterly lost in Western Christianity. As such, the Russian Orthodox tradition may be merged with Neopaganism and may host "Neopaganism's nationalist force, which anchors it in the Russian soil, and separates it from the two other Christian confessions".


title: Aleksandr Dugin

text: Dugin wrote a 1997 essay in which he described Soviet-era serial killer Andrei Chikatilo as a mystic and "a practitioner of Dionysian “sacraments" in which the killer/torturer and the victim transcend their "metaphysical dualism" and become one".


title: Aleksandr Dugin

text: In 1992, Eduard Limonov founded the National Bolshevik Front (NBF) as an amalgamation of six minor groups. Aleksandr Dugin was among its earliest members and was instrumental in convincing Limonov to enter politics, and signed the declaration of the founding of the party in 1993. The party first attracted attention in 1992 when two members were arrested for possessing grenades. The incident gave the NBP publicity for a boycott campaign they were organizing against Western goods.


title: Aleksandr Dugin

text: The NBF joined forces with the National Salvation Front (a broad coalition of Russian communists and nationalists). In 1998, Dugin left the NBP as a result of a conflict with other members of the party. This led to the party moving further left in Russia's political spectrum, and led to members of the party denouncing Dugin and his group as fascists.


title: Aleksandr Dugin

text: The Eurasia Party, which advances neo-Eurasianist ideas, was launched in April 2001. Dugin was reported as the group's founder. He said the movement would stress cultural diversity in Russian politics, and oppose "American style globalisation, and would also resist a return to communism and nationalism." It was officially recognized by the Ministry of Justice on 31 May 2001. The Eurasia Party claims support in some military circles and by leaders of the Orthodox Christian faith in Russia. The party hopes to play a key role in attempts to resolve the Chechen problem, setting the stage for Dugin's objective of a Russian strategic alliance with European and Middle Eastern states, primarily Iran.


title: Aleksandr Dugin

text: In 2005, Dugin founded the Eurasian Youth Union of Russia as the youth wing of the International Eurasia Movement.


title: Aleksandr Dugin

text: Dugin supports Russian President Vladimir Putin and his foreign policies but has opposed the Russian government's economic policies. He stated in 2007: "There are no more opponents of Putin's course and, if there are, they are mentally ill and need to be sent off for clinical examination. Putin is everywhere, Putin is everything, Putin is absolute, and Putin is indispensable". It was voted number two in flattery by readers of "Kommersant".


title: Aleksandr Dugin

text: In the Kremlin, Dugin represents the "war party", a division within the leadership over Ukraine. Dugin is an author of Putin's initiative for the annexation of Crimea by Russia. He considered the war between Russia and Ukraine to be inevitable and appealed for Putin to intervene in the War in Donbas. Dugin said: "The Russian Renaissance can only stop by Kiev."


title: Aleksandr Dugin

text: During the 2014 pro-Russian conflict in Ukraine, Dugin was in regular contact with pro-Russian separatist insurgents. He described his position as "unconditionally pro-DPR and pro-LPR". A Skype video call posted on YouTube showed Dugin providing instructions to separatists of South and Eastern Ukraine as well as advising Ekaterina Gubareva, whose husband Pavel Gubarev declared himself the Donetsk Region governor and after that was arrested by the Security Service of Ukraine.


title: Aleksandr Dugin

text: On 31 March 2014, Oleg Bahtiyarov, a member of the Eurasia Youth Union of Russia founded by Dugin, was arrested. He had trained a group of about 200 people to seize parliament and another government building, according to the Security Service of Ukraine.


title: Aleksandr Dugin

text: Dugin stated he was disappointed in President Putin, saying that Putin did not aid the pro-Russian insurgents in Ukraine after the Ukrainian Army's early July 2014 offensive. In August 2014, Dugin called for an eradication of Ukrainian identity.


title: Aleksandr Dugin

text: Halya Coynash of the Kharkiv Human Rights Protection Group said that the influence of Dugin's "Eurasian ideology" on events in eastern Ukraine and on Russia's invasion of the Crimea was beyond any doubt. According to Vincent Jauvert, Dugin's radical ideology became the basis for the internal and foreign policy of the Russian authorities. "So Dugin is worth listening to, in order to understand to which fate the Kremlin is leading its country and the whole of Europe."


title: Aleksandr Dugin

text: Ukraine gave Dugin a five-year entry ban, starting in June 2006, and Kyiv declared him a "persona non grata" in 2007. His Eurasian Youth Union was banned in Ukraine. In 2007, the Security Service of Ukraine identified persons of the Eurasian Youth Union who committed : they climbed up the mountain of Hoverla, imitated sawing down the details of the construction in the form of the small coat of arms of Ukraine by tools brought with them and painted the emblem of the Eurasian Youth Union on the memorial symbol of the Constitution of Ukraine. He was deported back to Russia when he arrived at Simferopol International Airport in June 2007.


title: Aleksandr Dugin

text: Before war broke out between Russia and Georgia in 2008, Dugin visited South Ossetia and predicted: "Our troops will occupy the Georgian capital Tbilisi, the entire country, and perhaps even Ukraine and the Crimean Peninsula, which is historically part of Russia, anyway." Afterwards he said Russia should "not stop at liberating South Ossetia but should move further," and "we have to do something similar in Ukraine." In 2008, Dugin stated that Russia should repeat the Georgian scenario in Ukraine, namely attack it. In September 2008, after the Russian-Georgian war, he did not hide his anger towards Putin, who "dared not drop the other shoe" and "restore the Empire."


title: Aleksandr Dugin

text: On 10 October 2014, Dugin said, "Only after restoring the Greater Russia that is the Eurasian Union, we can become a credible global player. Now these processes slowed down very much. The Ukrainian maidan was the response of the West to the advance of the Russian integration." He described the Euromaidan as a coup d'état carried out by the United States: "America wishes to wage the war against Russia not by its own hands but by the hands of the Ukrainians. Promising to wink at up to 10 thousand victims among the peaceful population of Ukraine and actually demanding the victims, the United States led to this war. The United States carried out the coup d'état during the maidan for the purpose of this war. The United States raised neo-Nazis Russophobes to the power for the purpose of this war."


title: Aleksandr Dugin

text: Dugin said Russia is the major driving force for the current events in Ukraine: "Russia insists on its sovereignty, its liberty, responds to challenges thrown down to it, for example, in Ukraine. Russia is attempting to integrate the post-Soviet space." As Israeli political scientist Vyacheslav Likhachov states, "If one seriously takes the fact that such a person as Alexander Dugin is the ideologist of the imperial dash for the West, then one can establish that Russia is not going to stop as far as the Atlantic Ocean."


title: Aleksandr Dugin

text: In the 2014 article by Dmitry Bykov "Why TV, Alexander Dugin and Galina Pyshnyak crucified a boy", Channel One Russia's use of the aired story by Dugin and Pyshnyak about the allegedly crucified boy as a pretext for escalating the conflict was compared to the case of Beilis. On 9 July 2014, Dugin on his Facebook account wrote a story that a 6-year-old child was allegedly nailed down to an advertisement board and shot to death before his father's eyes.


title: Aleksandr Dugin

text: On 16 July 2014, "Novaya Gazeta" provided a videotape of its correspondent Eugen Feldman walking along the main square in Sloviansk, asking local old women if they had heard of the murder of the child. They said such an event did not take place. The website Change.org hosted a petition of citizens who demanded "a comprehensive investigation with identification for all persons involved in the fabrication of the plot."


title: Aleksandr Dugin

text: On 2 October 2014, Dugin described the situation in Donbas: "The humanitarian crisis has long since been raging on the territory of Novorossiya. Already up to a million, if not more, refugees are in the Russian Federation. A large part of the inhabitants of the DPR and the LPR simply moved abroad." In the end of October 2014, Dugin advised the separatists to establish dictatorship in Novorossiya until they win in the confrontation.


title: Aleksandr Dugin

text: Dugin's influence on the Russian government and on president Vladimir Putin is disputed. He has no official ties to the Kremlin, but is sometimes referred to as "Putin's brain" or "Putin's Rasputin" and as being responsible for shaping Russian foreign policy. Others contend that Dugin's influence is limited and has been greatly exaggerated, on the basis that the correlations between his views and Russian foreign policy do not imply causation.


title: Aleksandr Dugin

text: Mark Galeotti, writing in 2022 for "The Spectator", noted that Western commentators tend to overstate the importance of Dugin in Russian politics, sometimes even describing him as a new Rasputin. In fact, his influence on the politics since 2016 was negligible, but Dugin tried to present himself as an influential person.


title: Aleksandr Dugin

text: In November 2022, the Latvian newspaper Meduza reported that, according to sources close to the Kremlin, Dugin's influence on Putin had grown after the killing of his daughter Daria Dugina. According to Meduza's interlocutors, the Western media had often exaggerated Dugin's political influence in the past, but after the murder of Dugina Putin had allegedly started to take a serious interest in his ideas and to use one of his favourite terms ("Anglo-Saxon") in a public speech.


title: Aleksandr Dugin

text: Dugin openly criticized Putin for failing to defend "Russian cities" such as Kherson, which was liberated from Russian control on 11 November 2022.


title: Aleksandr Dugin

text: Dugin made contact with the French far-right thinker Alain de Benoist in 1990. Around the same time he also met the Belgian Jean-François Thiriart and Yves Lacoste. In 1992 he invited some of the European far-right figures he had met into Russia. He also brought members of Jobbik and Golden Dawn to Russia to strengthen their ties to the country.


title: Aleksandr Dugin

text: According to the book "War for Eternity" by Benjamin R. Teitelbaum, Dugin met Steve Bannon in Rome in 2018 to discuss Russia's geopolitical relationships with the United States and China, as well as Traditionalist philosophy. Dugin also developed links with far-right and far-left political parties in the European Union, including Syriza in Greece, Ataka in Bulgaria, the Freedom Party of Austria, and Front National in France, to influence EU policy on Ukraine and Russia. Dugin is also closely aligned with Israeli journalist Avigdor Eskin, who previously served on the board of Dugin's Eurasia Party.


title: Aleksandr Dugin

text: The typical rhetoric about the fifth column as foreign agents is used by Dugin for political accusations in many publications. In his 2014 interview published by "Vzglyad" and "Komsomolskaya Pravda", he says, "A huge struggle is being conducted. And, of course, Europe has its own fifth column, its own Bolotnaya Square-minded people. And if we have them sitting idly and doing nasty things on Dozhd, Europe is indeed dominated and ruled by the fifth column in full swing. This is the same American riffraff."


title: Aleksandr Dugin

text: He sees the United States standing behind all the scenes, including the Russian fifth column. According to his statement, "The danger of our fifth column is not that they are strong, they are absolutely paltry, but that they are hired by the greatest 'godfather' of the modern world—by the United States. That is why they are effective, they work, they are listened to, they get away with anything because they have the world power standing behind them." He sees the US embassy as the center for funding and guiding the fifth column and asserts, "We know that the fifth column receives money and instructions from the American embassy."


title: Aleksandr Dugin

text: According to Dugin, the fifth column promoted the breakup of the Soviet Union as a land continental construction, seized power under Boris Yeltsin, and headed Russia as the ruling politico-economic and cultural elite until the 2000s. The fifth column is the regime of liberal reformers of the 1990s and includes former Russian oligarchs Vladimir Gusinsky, Boris Berezovsky, former government officials Mikhail Kasyanov, Boris Nemtsov, Vladimir Ryzhkov, artistic, cultural, and media workers, the Echo of Moscow, the Russian State University for the Humanities, the highest ranks of the National Research University Higher School of Economics, a significant part of teachers of the Moscow State Institute of International Relations, and a minority part of teachers of the Moscow State University.


title: Aleksandr Dugin

text: Dugin proposes to deprive the fifth column of Russian citizenship and deport the group from Russia: "I believe it is necessary to deport the fifth column and deprive them of their citizenship." However, in 2007, Dugin argued, "There are no longer opponents of Putin's policy, and if there are, they are mentally ill and should be sent to prophylactic health examination." In 2014, Dugin in an interview to "Der Spiegel" confirmed that he considers the opponents of Putin to be mentally ill.


title: Aleksandr Dugin

text: In one of his publications, Dugin introduced the term "the sixth column" and defined it as "the fifth column which just pretends to be something different", those who are in favor of Putin, but demand that he stand for liberal values (as opposed to the liberal fifth column, which is specifically against Putin). During the 2014 Russian military intervention in Ukraine, Dugin said that all the Russian sixth column stood up staunchly for Ukrainian oligarch Rinat Akhmetov. As he asserts, "We need to struggle against the fifth and sixth columns."


title: Aleksandr Dugin

text: Russian-American artist Mihail Chemiakin says Dugin is inventing "the sixth column". "Soon, probably, there would already be the seventh one as well. 'The fifth column' is understandable. That is we, intelligentsia, lousy, dirty, who read Camus. And 'the sixth column', in his opinion, is more dangerous, because that is the personal entourage of Vladimir Putin. But he is naïve and understands nothing. And as for Dugin, he can tell him who to shoot to death and who to imprison. Maybe Kudrin, and maybe Medvedev..."


title: Aleksandr Dugin

text: According to Dugin, the whole Internet should be banned: "I think that Internet as such, as a phenomenon is worth prohibiting because it gives nobody anything good." In June 2012, Dugin said in a lecture that chemistry and physics are demonic sciences, and that all Orthodox Russians need to unite around the president of Russia in the last battle between good and evil, following the example of Iran and North Korea. He added: "If we want to liberate ourselves from the West, it is needed to liberate ourselves from textbooks on physics and chemistry."


title: Aleksandr Dugin

text: Dugin has characterized his position on the Ukrainian conflict as "firm opposition to the Junta and Ukrainian Nazism that are annihilating peaceful civilians" as well as rejection of liberalism and US hegemony.


title: Aleksandr Dugin

text: In 2008 Dugin established a Center for Conservative Studies at the Moscow State University. The Center focused on counter-Enlightenment and conservative ideas of authors such as Guénon, Evola, Schmitt and Heidegger, and on their application to Russian politics. In 2014 Dugin lost that academic position due to the controversy following an interview where he commented on the death of 42 anti-Maidan activists in Odesa saying "But what we see on May 2nd is beyond any limits. Kill them, kill them, kill them. There should not be any more conversations. As a professor, I consider it so". Media outlets interpreted this as a call to kill Ukrainians. A petition entitled "We demand the dismissal of MSU Faculty of Sociology Professor A. G. Dugin!" was signed by over 10,000 people and sent to the MSU rector Viktor Sadovnichiy.


title: Aleksandr Dugin

text: Dugin claimed to have been fired from this post. The university claimed the offer of the position of the department head resulted from a technical error and was therefore cancelled, and that he would remain a professor and deputy department head under contract until September 2014. Dugin wrote the statement of resignation from the faculty staff to be reappointed to the Moscow State University staff due to the offered position of department head, but since the appointment was cancelled he was no longer a staff member of the faculty nor a staff member of the Moscow State University (the two staff memberships are formally different at the MSU).


title: Aleksandr Dugin

text: Dugin was named chief editor of Tsargrad TV by businessman Konstantin Malofeev soon after the TV station's founding in 2015.


title: Aleksandr Dugin

text: Dugin's first wife was Evgenia Debryanskaya, a Russian activist. They have a son, Artur Dugin, whom they named in honor of Arthur Rimbaud. Dugin had a daughter, Darya Dugina, with his second wife, philosopher Natalya Melentyeva. On 20 August 2022, Dugin's daughter Darya Dugina was killed in a car bombing when the car she was driving exploded near Bolshiye Vyazemy, a suburb of Moscow.


title: Aleksandr Dugin

text: On 11 March 2015, the United States Department of the Treasury added Dugin to its list of Russian citizens who are sanctioned as a result of their involvement in the Ukrainian crisis; his Eurasian Youth Union was targeted too. In June 2015, Canada added Dugin to its list of sanctioned individuals.


title: Aleksandr Dugin

text: On 3 March 2022 the United States Department of the Treasury sanctioned the outlet due to its alleged control by Dugin. Additionally, the United States Department of the Treasury sanctioned Dugin's daughter Darya on the basis of her work as chief editor of the website United World International (UWI). According to the United States Department of the Treasury, UWI was developed as part of Project Lakhta, owned by Yevgeny Prigozhin, who is held responsible for part of the Russian interference in the 2016 United States elections.


title: Aleksandr Dugin

text: Several of Dugin's books have been published by the publishing house Arktos Media, an English-language publisher for Traditionalist and New Right books.


title: Chilling Adventures of Sabrina (TV series)

text: Chilling Adventures of Sabrina is an American supernatural horror streaming television series developed by Roberto Aguirre-Sacasa for Netflix, based on the Archie comic book series of the same name. The series is produced by Warner Bros. Television, in association with Berlanti Productions and Archie Comics. Aguirre-Sacasa and Greg Berlanti serve as executive producers, alongside Sarah Schechter, Jon Goldwater, and Lee Toland Krieger.


text: The series is centered on the Archie Comics character Sabrina Spellman, portrayed by Kiernan Shipka, and also stars Ross Lynch, Lucy Davis, Chance Perdomo, Michelle Gomez, Jaz Sinclair, Tati Gabrielle, Adeline Rudolph, Lachlan Watson, Gavin Leatherwood, Richard Coyle, and Miranda Otto. Originally in development during September 2017 at the CW, the series was intended to be a companion series to "Riverdale"; however, in December 2017, the project was moved to Netflix with a straight-to-series order, consisting of twenty episodes. Filming took place in Vancouver, British Columbia.


text: The first half of the first season, consisting of ten episodes, was released on October 26, 2018. The series received positive reviews, with critics praising Shipka's performance, as well as the premise, visuals, and directing. A Christmas special episode was released on December 14, 2018, and the second half of the first season was released on April 5, 2019, consisting of nine episodes. In December 2018, Netflix renewed the series for a second season consisting of 16 episodes, split into two equal parts, of which the first eight episodes were released on January 24, 2020, with the second set released on December 31, 2020.


text: In July 2020, Netflix cancelled the series due to the COVID-19 pandemic. Two crossovers with "Riverdale" occurred during the sixth season of the latter series, providing closure to plot points from "Sabrina". A comic book series continuation, titled "The Occult World of Sabrina", was also announced.


text: "Chilling Adventures of Sabrina" is set in the fictional town of Greendale. It is a dark coming-of-age story that includes horror, fear and witchcraft. Sabrina Spellman must reconcile her dual nature as a half-witch, half-mortal while fighting the evil forces that threaten her, her family, and the daylight world humans inhabit.


text: In September 2017, it was reported that a live-action television series based on the comic book "Chilling Adventures of Sabrina" was being developed for the CW by Warner Bros. Television and Berlanti Productions, with a planned release in the 2018–19 television season. The series would be a companion series to "Riverdale". Lee Toland Krieger would direct the pilot, which would be written by Roberto Aguirre-Sacasa. Both are executive producers along with Greg Berlanti, Sarah Schechter, and Jon Goldwater. In December 2017, the project had moved to Netflix under a yet-to-be-announced new title. Two seasons, comprising ten episodes each, had been ordered by the streaming service; this was later altered to be one, 20-episode season split across two parts. CW President Mark Pedowitz stated that Netflix's ability to offer a two-season commitment enticed Warner Bros. Television to move the series to the streaming service. In early May 2018, "Chilling Adventures of Sabrina" was officially confirmed as the series' title. The series was inspired by "slow-burn horror" films such as "The Exorcist", "Rosemary's Baby", and other "great satanic horror movies from the 1960s and 1970s". The opening title sequence features the art of Robert Hack, the original artist of the comic book series.


text: On November 12, 2018, Netflix announced that the eleventh episode of the twenty episodes ordered would be released as a Christmas special episode. It was not always the plan for the series to have a Christmas-themed episode. During production of the first episode of the second part, Aguirre-Sacasa realized that the series had already done episodes related to Halloween and Thanksgiving in the first part, and decided to create the episode. He noted the episode "was by and large self-contained, but that there are still elements that carry it through and the realizations and relationships and mythology — it sort of threads the needle. And so we figured out a story that could do both." The episode was also helpful for Netflix, who wanted some sort of additional, standalone content to release between the first two parts. On December 18, 2018, Netflix renewed the series for a second season of 16 episodes, which was also split into two parts. On July 8, 2020, Netflix cancelled the series due to the COVID-19 pandemic.


text: In January 2018, Kiernan Shipka was cast as Sabrina Spellman. Shipka was Aguirre-Sacasa's first choice for the role. The next month, Jaz Sinclair was cast as Rosalind "Roz" Walker, along with Michelle Gomez as Mary Wardwell / Madam Satan, Chance Perdomo as Ambrose Spellman, Lucy Davis as Hilda Spellman, Miranda Otto as Zelda Spellman, and Richard Coyle as Father Faustus Blackwood. In March 2018, Ross Lynch joined the cast as Harvey Kinkle, while Tati Gabrielle was cast as Prudence Night. In early March 2018, Bronson Pinchot, Adeline Rudolph, and Abigail Cowen, were cast as George Hawthorne, Agatha, and Dorcas, respectively. In November 2018, it was revealed that Alexis Denisof and Jedidiah Goodacre would join the cast in the second part in the recurring roles of Adam Masters and Dorian Gray, respectively, while Mckenna Grace would portray a young Sabrina in the Christmas special episode.


text: In June 2019, it was reported that Lachlan Watson and Gavin Leatherwood had been promoted to the main cast for the second season. In December 2019, Sam Corlett, Skye Marshall, and Jonathan Whitesell were cast in recurring roles for part 3 of the series.


text: Filming for the first part began on March 19, 2018, just as filming of the second season of "Riverdale" concluded, which allowed the same crew members to work on both series. The first two parts were filmed back-to-back, with filming on the second part concluding on December 21, 2018. Filming had been expected to begin in February 2018 and last until June 2018. The first episode of the second part was the eleventh episode filmed, while the Christmas special was the twelfth episode filmed, despite the Christmas special being released as the eleventh episode overall in the series. This was because the idea for the Christmas special came about when the first episode of the second part was "too far down the line" to alter its production schedule. Despite the production switch, Aguirre-Sacasa said the first episode of the second part was written "as a premiere episode for the second part" and helps kick-off the storylines for the part. Production on the second season, consisting of the third and fourth parts, began on May 17, 2019, and concluded on February 22, 2020.


text: The series was originally conceived as a companion series to "Riverdale" when it was in development for the CW; however, after the series was moved to Netflix, it was unclear if any connection would remain. In January 2018, CW president Mark Pedowitz noted that, "at the moment, there is no discussion about crossing over." In March 2018, Jon Goldwater confirmed that the two series were "two separate entities for right now" but "would love it if they could figure out a way to cross over." Goldwater also felt there was a possibility for the characters to appear on future episodes of "Riverdale", since Greendale had already been mentioned as existing on that series.


text: Sabrina's town, Greendale, is introduced in the second season of "Riverdale". Following that, several references to the two cities are made regularly in the two series, visually or with dialogues. In the first season of "Chilling Adventures of Sabrina", Moses Thiessen reprises his role as Ben Button from "Riverdale" during an episode. In the episode "Chapter Sixty-Seven: Varsity Blues" from the fourth season of "Riverdale", Ty Wood reprises his role as Billy Marlin from "Sabrina".


text: In episode "Chapter Twenty-Three: Heavy Is the Crown" from the third part of "Sabrina", the teenage witch and her cousin visit Riverdale in search for a crown that was owned by Benjamin Blossom, an ancestor of Cheryl. On their way, they pass the town sign. On its back, Jughead Jones spray painted the message "JJ Wuz Here", his signature. Three episodes later, a member of the Southside Serpents is attacked by Hilda Spellman.


text: In episode "Chapter Thirty-Four: The Returned" from the fourth part of "Sabrina", a battle-of-the-bands poster lists the "Fred Heads" as an entrant in the competition. This was the name of the high school garage band of Archie's father Fred Andrews.


text: Regarding a proper crossover, Aguirre-Sacasa said in October 2018 he would "hate [for a crossover] to never happen" between the two series, adding that a potential idea for one would see the characters of "Riverdale" "hear[ing] about a haunted house in Greendale and try[ing] to break in and it's Sabrina's house". He also stated that since both series were already established, a crossover could happen in a standalone film with both casts, potentially titled "Afterlife with Archie", based on the Archie Horror comic book series of the same name.


text: On October 7, 2021, it was announced that Shipka would be reprising her role as Sabrina in the sixth season of "Riverdale". During the same season, the series introduced the character Heather, played by Caroline Day, a witch from Greendale and from Sabrina's coven.


text: In November 2018, Satanic Temple activists sued the series' production team over the use of the Statue of Baphomet, which they claim was a direct copy of their own statue and portrayed the Temple in an inaccurate and derogatory way. Temple members were also concerned about the depiction of Satanists as cannibals practicing forced worship. On November 21, 2018, it was confirmed that Satanic Temple and Netflix had made a pact and amicably settled the lawsuit dispute, with the terms of the deal left undisclosed to the public.


text: On March 15, 2019, WaterTower Music released a digital EP with four songs performed by some of the members of the series' cast during the first part of the first season. A compilation of songs from the first season, including six songs performed by the cast (four from the EP and two new songs), was released on digital by WaterTower Music on April 5, 2019. Soundtrack from the first part of the second season was released on January 24, 2020, followed by the soundtrack for the last part on January 1, 2021.


text: An album of Adam Taylor's scoring for season 1 was released on compact disc by La-La Land Records, and simultaneously on download by WaterTower Music, on August 16, 2020. The soundtrack and score from the first season was released by Waxwork Records in 2020 on 180 gram vinyl, which was a triple LP.


text: The first ten episodes of "Chilling Adventures of Sabrina" were released worldwide on Netflix on October 26, 2018. The same day, the first two episodes were shown in a special screening at Paris Comic-Con 2018. The eleventh episode of the first part, a Christmas special episode, was released on December 14, 2018. The remaining nine episodes of the first season were released on April 5, 2019. The first part of the second season, dubbed Part 3, was released on January 24, 2020. The second part of the second season, also the last part of the series, dubbed Part 4, released on December 31, 2020.


text: For the first part of the first season, the review aggregator website Rotten Tomatoes reported a 91% approval rating with an average rating of 7.77/10 based on 103 reviews. The website's consensus reads, "Bewitchingly beautiful and wickedly macabre, "Chilling Adventures of Sabrina" casts an intoxicating spell and provides a perfect showcase for Kiernan Shipka's magical talents." Metacritic, which uses a weighted average, assigned a score of 74 out of 100 based on 28 critics for the first part of the first season, indicating "generally favorable reviews."


text: Alicia Lutes of "IGN" gave part one a 9.2/10, saying that it "shines in its deliciously dark plotlines, volumes of camp, and irreverent and at-times antagonistic humor." Dave Nemetz of TVLine gave part one a "B+" saying that ""Sabrina" is more tongue-in-cheek and self-aware than "Riverdale" is ever allowed to be" and that it is "off to a bewitchingly great start." Meagan Navarro from Bloody Disgusting praised part one, stating that it is "fun and briskly paced".


text: Daniel Fienberg from "The Hollywood Reporter" stated in a review of part one, that the "appeal of Sabrina, increasing as the show goes along, comes mostly from Shipka". He praises the actress's performance by mentioning that she is "perfectly cast complement to one of the show's most endearing elements, namely its blurry approach to modernity. Chris Hayner from "GameSpot" praised part one by highlighting the performances of the cast members. He further complimented the progressive undertones of the series and stated that it "manages to tangle with modern day issues many face, while couching it all in a supernatural world". Constance Grady from "Vox" praised part one, particularly for its cinematography, stating that its "higher production values are apparent in every frame, and the result is gorgeous". She further added that when the series fully commits to its dark goth horror aesthetic, it is at "its most thrilling." Petrana Radulovic from "Polygon" stated in her positive review of part one that "once the horror kicks in, the season continues with just as much chills and sets the stage for what comes next."


text: For the Christmas special episode, Rotten Tomatoes reported a 76% approval rating with an average rating of 6.56/10 based on 21 reviews. The website's consensus reads, "This holiday chapter from Sabrina's "Chilling Adventures" spikes the eggnog with the series' ghoulish sensibility, but viewers may feel disappointed by the special's confusion over whether it is a self-contained diversion or a continuation of the series' core story."


text: The seventh episode of the first season is particularly controversial for its depiction of a teenage orgy.


text: The second part of the first season received an average of 6.88 out of 10 on Rotten Tomatoes, with an overall 81% approval based on 43 reviews. The website's consensus reads, "With a stronger mystery steeped in witchy world-building, "Chilling Adventures" remains a deliciously dark, delightfully campy romp that pushes Sabrina deeper down the path of night — if only she would get there a little faster."


text: Rotten Tomatoes reports that 90% of 29 critic ratings are positive for the part three, with an average rating of 7.36/10. The website's critical consensus reads, "A deliciously hellish thrill ride from start to finish, "Chilling Adventures of Sabrina" just keeps getting better."


text: On Rotten Tomatoes, part four has an approval rating of 67% based on reviews from 24 critics, with an average rating of 7.13/10. The website's critical consensus states, "Though it leaves some fan favorites high and dry, "Chilling Adventures of Sabrina" final season hits enough emotional highs to serve as a fitting farewell to the Queen of Hell."


text: Following the series' cancellation, Kiernan Shipka reprised her role as Sabrina in the episode "Chapter Ninety-Nine: The Witching Hour(s)" from the sixth season of "Riverdale". The episode is set in an alternative universe called Rivervale where Sabrina is called by Cheryl Blossom (Madelaine Petsch) to help her with a spell. Shipka also reprised the role in "Chapter One Hundred and Fourteen: The Witches of Riverdale" during the same season, an episode set in the original continuity of the two series and after the events of "Chilling Adventures of Sabrina". The episode provides closure to plot points from the series. Nicholas Scratch also appeared in the episode, portrayed by Cole Sprouse, following a temporary resurrection spell used on Jughead Jones's body.


text: In July 2021, it was announced that the prospective fifth part and third season would be published as the comic book sequel series "The Occult World of Sabrina". The first arc of the series will finish the “World Without Sabrina” storyline that began at the end of the series finale.


text: Roberto Aguirre-Sacasa also announced that a comics crossover with "Riverdale" and another one with the original comic book series are also being considered.


title: Fall Out Boy

text: Fall Out Boy is an American rock band formed in Wilmette, Illinois, a suburb of Chicago, in 2001. The band consists of lead vocalist and rhythm guitarist Patrick Stump, bassist Pete Wentz, lead guitarist Joe Trohman, and drummer Andy Hurley. The band originated from Chicago's hardcore punk scene and was formed by Wentz and Trohman as a pop punk side project; Stump joined shortly thereafter. The group went through a succession of drummers before Hurley joined. Their debut album, "Take This to Your Grave" (2003), became an underground success and helped the band gain a dedicated fanbase through heavy touring. "Take This to Your Grave" is cited as influential on pop punk music in the 2000s.


title: Fall Out Boy

text: With Wentz as the band's lyricist and Stump as the primary composer, Fall Out Boy's 2005 major-label breakthrough, "From Under the Cork Tree", produced two hit singles, "Sugar, We're Goin Down" and "Dance, Dance". It went double platinum, transforming the group into superstars and making Wentz a celebrity and tabloid fixture. Fall Out Boy received a Best New Artist nomination at the 2006 Grammy Awards. "Infinity on High" (2007) debuted at number one on the "Billboard" 200 with 260,000 first week sales. It produced two worldwide hit singles, "This Ain't a Scene, It's an Arms Race" and "Thnks fr th Mmrs". "Folie à Deux (2008)", was a commercial disappointment and received a mixed response. Following the release of "Believers Never Die – Greatest Hits" in 2009, the band went on hiatus and the members worked on side projects.


title: Fall Out Boy

text: "Save Rock and Roll" (2013) became Fall Out Boy's second number-one album, and included the top 20 single "My Songs Know What You Did in the Dark (Light Em Up)". The same year, the band released the EP "PAX AM Days", consisting of 8 punk-influenced tracks that were recorded during a two-day session with producer Ryan Adams. The band's sixth studio album, "American Beauty/American Psycho" (2015) peaked at number one on the "Billboard" 200, and spawned the top-10 hit "Centuries" and the single "Uma Thurman" which reached No. 22 on the "Billboard" Hot 100. This was followed by their first remix album "Make America Psycho Again", which featured the remixes of all original tracks from "American Beauty/American Psycho" by a different artist on each song, including Migos and Wiz Khalifa.


title: Fall Out Boy

text: The band's seventh studio album "Mania" (2018), also peaked at No. 1, making it the band's fourth No. 1 album and sixth consecutive top 10 album. The Mania tour included a show at Wrigley Field, their first headlining stadium show. In 2018, Fall Out Boy also received their second Grammy nomination for Best Rock Album for "Mania". A co-headlining 2020 tour with Green Day and Weezer titled the "Hella Mega Tour" was announced in September 2019. Each band released new music in support of the tour, with Fall Out Boy announcing the release of a second greatest hits album, "", and a supporting single, "Dear Future Self (Hands Up)". The COVID-19 postponed tour, which spans North America, and Europe, is Fall Out Boy's first stadium tour and includes shows in Wrigley Field, Dodger Stadium and the London Stadium.