this application claims the benefit of u . s . provisional application no . 60 / 519720 , filed nov . 12 , 2003 and u . s . provisional application no . 60 / 520873 , filed nov . 18 , 2003 . ( 35 usc 119 ( e )). an arrangement of a set of sheets made from openwork material , such as but not limited to wirecloth , is pigmented so that one of each of the additive primaries is clearly visible from a plurality of domains of the openwork surface , and the plurality of domains from which each primary is visible being about ⅓ the whole of this surface . for asymmetric forms , the size of the domains covered by a primary may change with respect to the asymmetry of the arrangement . for instance if the cube in fig2 were increased in the y dimension , the colors occupying the faces extended in y might also increase . the sheets are arranged so that an observer will see pairs of sheets superposed and pairs from the group of the primaries at any viewing angle , except where an opaque presentation base or support for the sheets may naturally obscure viewing . the members of the set of sheets are joined by such means as , but not limited to , hinges , rotational axles , pegs , fusing the material , knotting , twisting , bending . the arrangement of sheets is positioned against a field of zero , or near zero luminance ( such as black velvet and which may also include darkening the room in which the arrangement is presented ), and illuminated for viewing with one or more incidental white light sources . a spotlight , sunlight , or a bright halogen light work well — a second or third light from different angles will help eliminate shadows . ( in this case shadows are an unintentional interference ). the reflected colors of two overlapping regions stimulate responses of secondary and tertiary colors . at an appreciable distance , an observer in motion with respect to the arrangement of the sheets will naturally experience parallax between the sheets &# 39 ; nearer and firther regions . a walk around the arrangement prompts an observer to discover that the same domain of any one primary color contributes , by superposition over one or the other primary domains behind it , to the product of two different secondary colors . these colors alternate as the observer moves around the arrangement . to effect the same alternations , the arrangement itself can also be made to turn by a variety of means . the parallax is most dramatic when the sheets are arranged as planes meeting at 90 ° to one another . an observer moving around a set of planes constructed as the cube in fig1 with the primaries arranged as in fig2 will discover different ratios of the three primaries [ b , g , r ]. the density of one color arriving at the retina from the inside of a posterior surface , increases as the viewing angle with respect to that surface &# 39 ; s plane approaches 0 °. the increased density of this colored light passes through the open regions of the face nearest the viewer , which is 90 ° to the former . this allows for different ratios of the two primaries . the varying ratios of two different primaries produce variants of the secondary colors — the tertiaries . if the arrangement forms a hexahedron , there are five possibilities for positioning the colors , one of which was shown in the provisional application . if the three primaries are arranged so that identical primaries appear on adjacent faces , then a view along a line joining two corners shows the circular sequence of the spectrum [ fig2 ]. the shadows cast by the openwork nearest the source or sources of light effect the amount of color visible from other domains . if the openwork &# 39 ; s apertures are proportionally small with respect to its material surface area , allowing less light to pass , the amount of color visible from domains behind it diminishes ( unless independently illuminated ). thus the openwork of the sheets must be consistent for an effect that works similarly from all angles of viewing . a wire diameter of about 12 - 15 % of the open width of a unit of wire cloth works well in the case exhibited in fig1 , however the openwork may be inconsistent to produce variations of the color generating effects . ultimately it is the separation of the primaries allowed by the openwork which plays a crucial role in the sensation of clean secondary colors from pigments of these additive primaries . sheets may be of unit value of the openwork , i . e . polygons or circles . the lattices may also be applied as opaque inks or paint to a clear substrate . while technically not as effective as the above description , a cube with transparent lattices of the primaries show a pleasing effect . derivatives of the invention might include lattices of emissive light . three primaries of laser light could be reflected as a mesh along a mirrored framework to reflect their light in a vapor or gas cloud . fig3 shows a comparative study — the object constructed as above , but reflecting one additive primary ( blue , green , or red ) and its secondary complement ( yellow , magenta , or cyan ) will produce white against a black ground . the spinning top illustrated in fig5 has a rigid disc [ 2 ] fixed between the spheroid base [ 1 ] and the shaft or spindle [ 3 ]. the disc has three functions : a ) it serves as a platform for pigment versions of the three additive primaries , red [ r ], green [ g ], and blue [ b ], which appear as three equally - sized sectors of the disc ; b ) the disc acts as a stabilizer limiting the inclination of the top &# 39 ; s axis ; c ) it provides a convenient place for a small repositionable weight or weights [ 4 ] to be applied and relocate the center of mass of the top . once the top is spinning , the primary function of the shaft [ 3 ] is to provide shadows and break the sequence of colors . it can be white , black , or a vertical continuation of the primaries appearing on the disc , but a non - intrusive color , such as natural wood is best . a clear matte finish shaft for plastic versions of the top is interesting but not as effective as opaque variety . the base of the spinning top plays little role in the color effects and may be any color that does not cancel the effects of the colors on the disc . for variations and nuance of colors , the sectors [ r ], [ g ], [ b ] in fig4 may be increased or decreased slightly . u . s . provisional application no . 60 / 519720 stated the proportions of the top and they are essentially the same as specified in this disclosure . the general proportions to obtain the desired motion can be inferred from the example provided here , which assumes a solid hardwood base [ 1 ] of 31 . 75 mm diameter by 23 . 8125 mm height , a disk [ 2 ] of similar solid material ( such as basswood ply ) in the range of 47 . 5 mm to 54 mm in diameter by 1 . 6 to 2 mm thick , and a shaft [ 3 ] of similar solid material with a length ranging from about 25 mm to 32 mm , with diameter 6 . 35 mm fig5 shows one clip weight [ 4 ] applied to the disc , and the center of mass shifted slightly from a location [ m 1 ] above the base &# 39 ; s radial center [ q ], to a point [ m 2 ] in the direction of the weight . when spun , the top inclines and turns about a new axis between the radial center [ q ] and the center of mass [ m 2 ] in such way as to create , at various locations in the sweep of the top &# 39 ; s motion , different ratios of the three primaries and the zero color factor . the locations of the primaries on the disc are referenced as letters [ r ], [ g ], [ b ]. fig6 through 9 show one type of rotation the top will make , and represent quarter - period positions of the top over one period . the locations of the primaries on the disc as the top turns around the vertical axis p [ p ] are referenced as letters [ r ], [ g ], [ b ]. when the top is set in motion near a lamp located forty - five degrees to p , an observer also forty - five degrees to axis p but ninety degrees to the lamp , will see a cone of ellipses formed by the moving disc , and a cone formed by the shaft [ 3 ]. the observer will also see several new regions of color other than the primaries . there is an upper region of color occurring toward the back of the disc &# 39 ; s sweep , a lower region of color occurring toward the front of the disc &# 39 ; s sweep , two colored regions in the shadows cast on the disc by the shaft , and two colored regions at the extreme positions of the shaft itself . the regions of secondary colors related to the shaft and its shadows , are indicated in italics [ y ] and [ k ]. the two regions of color at the disc &# 39 ; s upper and lower extremes are not referenced in the figures but can be inferred by examining the disc &# 39 ; s orientation across the horizontal dimension and summing the occurance of primary colors for a point in the disc &# 39 ; s sweep but relative to the top &# 39 ; s motion . ( the figures are aligned horizontally along the focus of the cycle ). in fig6 through 9 , the colors would be cyan in the disc &# 39 ; s lower region and red in the upper . used under ordinary incidental white light , but preferably against a dark field under an incandescent spotlight ( with a bit warmer hue than sunlight and which casts crisp shadows ), the range of colors produced includes magentas , violets , blues , cyans , greens , yellows , oranges , and reds . variations in the degree of inclination , the period , or periods , between maximal and minimal inclination , and whether or not the top spins around its geometric axis ( axis of structural symmetry through the shaft ) during its rotation around axis p , may arise from the nature of the materials used for construction . the top made from hardwood and ply , ( 0 . 00065 grams per cubic millimeter ), tends to either change angle and color in regular intervals ( rocking ), or stabilize at a constant angle until a disturbance interrupts it . the stabilized top constructed from lighter materials generally does not also spin around its own axis of symmetry during the rotation around p , except when there is a change in its inclination due to such a disturbance or change in equilibrium . in the steady state the top does not exhibit a classic precession and therefore exhibits no shifts in the observed secondary colors . the arc of the base allows smooth transitions between inclination changes but also allows the top to travel laterally across the surface upon which it spins , so a dish is helpful to contain it . the same device made from a heavier wood or uniform material like acrylic ( 0 . 00118 grams per cubic millimeter ), can be balanced to produce a progressive precession which gradually falls to about 30 °, or even 40 ° from vertical . these tops also spin around their own axes during precession . ideally the tops might be made of a plastic with the same density of the hardwood , providing consistency in manufacturing , but the irregularities of wood make each one slightly unique . the top should be spun under adequate illumination ( but preferably not fluorescent ), and while not consequential to the effectiveness of the device , spinning on a dark surface enhances one &# 39 ; s perception of the colors . to best see the colors , the top should be spun very fast . in bright sunlight a fast spinning speed is essential . as an alternative to the repositionable weight [ 4 ], a bit of wax can also be placed under the disc to alter the resulting geometric image and color effects . the top can be spun with a launcher the additive primary red [ r ] indicated in this specification and in the figures reflects wavelengths 570 - 700 nm with peak values starting near 620 nm . the additive primary green [ g ] indicated in this specification and the figures reflects wavelengths 500 - 650 nm with peak values near 550 nm . the additive primary blue [ b ] indicated in this specification and the figures reflects wavelengths 400 - 700 nm with peak values near 440 nm . an alternative blue [ b ] reflects wavelengths 400 - 700 nm with two peak values , one near 440 nm and the second near 510 ( cobalt has a third curve near 700 but it is hard to notice with the naked eye ). the primaries red , green , and blue , can be made from a number of fundamental coloring agents . the author has obtained them using the following pigments : ultramarine ( pb 29 ); cobalt blue ( pb 28 ); cadmium reds ; cadmium oranges ; cadmium yellows ; naphthol red light ( pr 112 ); irgazine red ; irgazine orange ; arylide yellow ( py 73 gx ); arylide yellow ( py 3 ); phthalocyanine green ( pg 7 ); zinc white ( pw ); titanium white ( pw 6 ); aluminum oxide . the values of all three primaries , red , green , and blue , indicated above , may vary to some degree , but it is important their relationship be consonant . the naturally dark blue pigments used to make the primary blue , in all cases of the specified invention , have been modified with white in order to bring that value within range of the red and green , such that on a value scale from 1 to 10 , where red is near 6 , and green near 5 , then blue will be near 4 . likewise , if the values for red and green are near 7 and 6 , then blue would be near 5 .