This paper applies the mathematics of chaos to the task of designing indoor rock-climbing routes. Chaotic variation has been used to great advantage on music and dance, but the challenges here are quite different, beginning with the representation. We present a formalized system for transcribing rock climbing problems and then describe a variation generator that is designed to support human route-setters in designing new and interesting climbing problems. This variation generator, termed strange beta, uses chaos to introduce novelty. We validated this approach with a large blinded study in a commercial climbing gym, in cooperation with experienced climbers and expert route setters. The results show that strange beta can help a human setter produce routes that are at least as good as, and in some cases better than, those produced in the traditional manner.
As mentioned above, the use of computers in creative tasks---for independent generation and or in assistance roles---is not a new idea. Computation has a particularly rich history in music composition, in both generative and assistant roles @cite_19 . Route setting for indoor climbing is viewed by its practitioners as a creative task on par with music composition, requiring substantial expertise in order to create routes that are both of an appropriate difficulty and interesting to climb. A climbing route is a prescribed sequence of dynamic movements: a sequence of symbols from a complex language not unlike a dance or a tonal music composition, both of which can also be viewed as symbol sequences. All three of these domains---climbing, music, and dance---have strong notions of style,'' but that notion is very hard to formalize, even for experienced practitioners.
@cite_19
1968754505 2160001073 2744457411 2627058984
Stylistic composition is a creative musical activity, in which students as well as renowned composers write according to the style of another composer or period. We describe and evaluate two computational models of stylistic composition, called Racchman-Oct2010 (random constrained chain of Markovian nodes, October 2010) and Racchmaninof-Oct2010 (Racchman with inheritance of form). The former is a constrained Markov model, and the latter embeds this model in an analogy based design system. Racchmaninof-Oct2010 applies a pattern discovery algorithm called SIACT and a perceptually validated formula for rating pattern importance, to guide the generation of a new target design from an existing source design. A listening study is reported concerning human judgments of music excerpts that are, to varying degrees, in the style of mazurkas by Frederic Chopin (1810–1849). The listening study acts as an evaluation of the two computational models and a third, benchmark system, called Experiments in Musical Intelligence. Judges’ responses indicate that some aspects of musical style, such as phrasing and rhythm, are being modeled effectively by our algorithms. Judgments are also used to identify areas for future improvements. We discuss the broader implications of this work for the fields of engineering and design, where there is potential to make use of our models of hierarchical repetitive structure. A common task in dance, martial arts, animation, and many other movement genres is for the character to move in an innovative and yet stylistically consonant fashion. In this paper, we describe two mechanisms for automating this process and evaluate the results with a Turing Test. Our algorithms use the mathematics of chaos to achieve innovation and simple machine-learning techniques to enforce stylistic consonance. Because our goal is stylistic consonance, we used a Turing Test, rather than standard cross-validation-based approaches, to evaluate the results. This test indicated that the novel dance segments generated by these methods are nearing the quality of human-choreographed routines. The test-takers found the human-choreographed pieces to be more aesthetically pleasing than computer-choreographed pieces, but the computer-generated pieces were judged to be equally plausible and not significantly less graceful. Musical or choreographic variation—one of the most fundamental of compositional techniques—are based upon two phases of work: establishment of a grounding theme and a series of structured departures from that theme. Classic examples are Bach's Goldberg Variations for the keyboard or Balanchine's The Four Temperaments ballet. The properties of dynamical chaos provide unusual mechanisms for achieving these effects. The characteristic patterns of strange attractors can be used to capture the underlying theme of the sequence and chaos's sensitive dependence on initial conditions can be used to produce variations. This intriguing notion was proposed by Diana Dabby in the mid-1990s in the context of music and image (1, 2). Inspired by Dabby's work, we set out to apply some similar ideas to dance. The result was the pair of tools that are described in this paper: CHAOGRAPHER, which produces chaotic variations of keyframed movement sequences, and MOTIONMIND, which extracts the patterns from a corpus of movement sequences and uses those patterns to generates original and yet stylistically consonant movement. These two tools, working together, can produce novel, interesting movement. The core of CHAOGRAPHER's strategy for introducing novelty is to create a mapping that associates a sequence of body positions with a chaotic attractor, and then use that mapping to generate variations. The fixed attractor structure guarantees that the variations will resemble the original in a mathematically precise sense, while sensitive dependence on initial conditions guarantees Automatic music generation systems have gained in popularity and sophistication as advances in cloud computing have enabled large-scale complex computations such as deep models and optimization algorithms on personal devices. Yet, they still face an important challenge, that of long-term structure, which is key to conveying a sense of musical coherence. We present the MorpheuS music generation system designed to tackle this problem. MorpheuS' novel framework has the ability to generate polyphonic pieces with a given tension profile and long- and short-term repeated pattern structures. A mathematical model for tonal tension quantifies the tension profile and state-of-the-art pattern detection algorithms extract repeated patterns in a template piece. An efficient optimization metaheuristic, variable neighborhood search, generates music by assigning pitches that best fit the prescribed tension profile to the template rhythm while hard constraining long-term structure through the detected patterns. This ability to generate affective music with specific tension profile and long-term structure is particularly useful in a game or film music context. Music generated by the MorpheuS system has been performed live in concerts. Machine improvisation and related style simulation problems usually consider building repre- sentations of time-based media data, such as music, either by explicit coding of rules or applying machine learning methods. Stylistic learning applies such methods to musical sequences in order to capture salient musical features and organize these features into a model. The Stylistic simulation process browses the model in order to generate variant musical sequences that are stylistically consistent with the learned ma- terial. If both the learning process and the simulation process happen in real-time, in an interactive system where the computer “plays” with musicians, then Machine Improvisation is achieved. Improvisation models have to cope with a trade-off between completeness (all the possible patterns and their continuation laws are discovered) and incrementality (the completeness is ensured only asymptotically for infinite sequences). In a previous work we devised a complete and incremental model based on the Factor Oracle Algorithm. In this paper we propose a concurrent constraints model for the Factor Oracle and show how it can be used in a concurrent learning improvisation situation. Our model is based on a non-deterministic concurrent constraint process calculus (NTCC). Such an approach allows the system to respond in a faster and more flexible manner to real-life performance situations. In addition, the declarative nature of constraints greatly simplifies the expansion of the system with improvisation rules at a higher musical level. We also describe the implementation of our model in a NTCC interpreter written in Common Lisp that is capable of real time performance.