DIFFUSELY-REFLECTIVE ADDITIVE-PRIMARY COLOR GENERATORS

PREAMBLE

It has been said that one cannot understand color without being confused. I was inclined to believe it after more than two decades of working with color in a practical manner, first in traditional visual arts and then on-screen, and still not fully understanding the relationship between the additive and subtractive color systems.

One intuitively grasps how to work within the rules of one color system or the other, but understanding the divide between the two systems requires sorting through a nearly universal assumption that the additive system applies to emitted color, and the subtractive system applies to reflected color. Another factor contributing to the confusion about color is that despite our everyday familiarity with it, we still don't really know what color is.

What is color? Where is the experience of color located? Only in our minds? Do colors even have a place? Are colors fictional? Are they psychological? Are they emotions? Mere affects? Or is there a physical component to color? A hard and fast thing"? Does color exist in light itself? It has long been held that light itself has no color. That is, light waves or light particles are colorless until we experience the color they stimulate. So, are colors triggered by light, called up or pointed to, as if we have a supply of colors like a box of crayons somewhere in our brains, and the colorless light particles arriving at the retina tap out a code like "row eight, column three" and once this information has been channeled through a network of neurons the brain just pops up the color located at "row eight, column three?" There it is in the middle of our mind, the color at "row eight, column three." How does that work? One could follow this reasoning and suggest that colors are ideals. Perhaps there exists a vault of colors in another realm, buried in a collective subconscious to which we all have access and enter when the wavelengths in a black and white world indicate the right combination.

Where and when does the colorless become colorful? Do retinal pigments first translate the colorless energy, into the colorful energy? Are they subsequently passed along from neuron to neuron, like batons in a relay race? Yet we dream in color. So does color appear further along stream?

How can we determine that an apple is not red until we see it? Centuries ago, when it was first claimed that visible light is actually colorless, it was not known that light is absorbed and emitted by electrons, which are also the foundations of neural communication. If our minds and the world we observe are but different manifestations of the same constituents, operating under the same set of rules, and if light is absorbed and emitted by electrons, then we should be permitted to question whether or not certain frequencies of energy possess color, or are color. Might colors, at least three of them, be no less reducible than other aspects of our world we consider to be irreducible, like dimensions?

These are the kinds of thoughts I had, and questions I asked myself when I began to investigate the difference between additive and subtractive color processes. Below are a few of the observations I have made in my search for answers.

BACKGROUND

By manipulating the luminosity function involved in color perception, the presented process (hereafter called the 'Process') links the additive-color system normally associated with emissive light, to the subtractive-color system normally associated with diffusely-reflected light.

Given that a single swatch of opaque reflected color (pigment and paint of all varieties) seems brighter when placed against a black background, the author observed that the perceived mixture of two superposed arrays of color, each of a different diffusely-reflected additive-primary red (R), green (G), or blue (B) also seems brighter when superposed with an array of black, or zero retinal stimulation.

The Process introduces intervals of black into otherwise low-level color stimuli arriving from RGB primaries diffusely reflected under incidental white light for the purpose of elevating the perceived luminance of the primaries to a degree that their mixtures, the secondary and tertiary colors, are also elevated. The modulation of intervals of zero light stimuli which seems to raise the perceived value of the additively generated combinations is one of the essential differences between this process and the prior art. Further investigations invited other differences which underlie the chromatics of three types of polychrome sculpture the author has created. The Process may also be helpful to the educational and scientific communities and may be utilized commercially to add novelty or intrigue to various products.

It will be helpful to briefly review the types.

Type I is nearly static and employs pointilistic color-mixing by means of diffusely-reflected RGB stimuli converging on the retina. Ratios of the primaries stimulating sensations of secondary and tertiary colors are created by overlapping domains of opaque red (R) green (G) or blue

(B) elements comprising openwork structures — for secondary colors these domains are in pairs — against black backgrounds under incidental white light. Changes in the ratios of these stimuli are controlled by changes in orientation of the overlapping domains of R, G, or B. Parallax between anterior and posterior portions of a three-dimensional openwork structure is a natural occurrence for an observer in motion with respect to the structure and is an easy method of effecting this change.

Type II is characterized by rapid movement in which areas of the retina are stimulated first by one diffusely-reflected red (R) green (G) or blue (B) primary, then by a second, followed by a period of low or zero stimuli. In the example below the primaries are modulated by rotation through three dimensions of a plane tri-sectored in RGB (opaque). It is a variety of spinning top.

Type 111, a synthesis of 1 and II, is characterized by rapid movement of openwork structures which occupy two or three dimensions. In Type III, the chromatic change is modulated by a static system

90 of lines or points of RGB which is then rotated through only two dimensions. The integration of black occurs either through spaces between the colored elements, as in Type I, or located adjacent to, and moving with, the colored elements.

Background for the Openwork Generators

95

It is generally assumed that color-mixing under incidental white light is subtractive, with primaries of a cool blue, yellow and cool red, or cyan, yellow, and magenta, whereas emissive and transmis- sive color-mixing is additive, with primaries of a warm red, yellow green, and reddish blue. One cannot make a bright yellow from red and green by stirring red and green paints together. This

100 produces a rust color. Stirring paints or overlaying transparent inks allows the absorption, or cancellations, of the reflected colors of neighboring particles, which darkens the total reflection. In the case of stirring green and red pigment particles together, the green particles will subtract some of the red light reflecting from the red particles, and likewise, the red particles will subtract some of the green light reflecting from the green particles. Neither can one achieve yellow by

105 filtering green light through a red glass. A red filter, absorbing all colors except red, will absorb the green light.

By projecting two sources of white light, one through a green filter and the other through a red filter so they converge at the retina, or first upon a white screen and then to the retina, yellow will be the 110 result. Similarly, a field of dots of red and green paint placed side by side (pointillism), produces a better yellow than stirring paints of the two colors. But the apparent low level of diffusely-reflected color, as compared to the brightness of color emitted from a source like a TV or computer screen, diminishes the results in either case.

115 Current theories of vision broadly divide our perception of luminosity and color into two different retinal responses from receptor cells that are sensitive to any light (rods), and color receptors (cones) sensitive to specific frequencies. Before responses are sent to the brain, a network of ganglion cells channels these receptors' input. Ganglion cells, among others, possess concentric zones of sensitivity, called receptive fields, which may cover relatively large regions (lmm)

120 of receptor cell signals. Variables in the light stimulus, such as intensity, size, and location of the stimulus within the cell's receptive field, determine whether the cell is excited or inhibited. Ganglion cells respond weakly when input from their connected receptors covers the ganglion's entire receptive field, but strongly when the input is localized to a specific region in the field. ¹ The color response is apparently also of a lower resolution than the light/dark response. ² When colored

125 dots (as in a color halftone photograph) appear smaller than the retina's receptive fields, the eye can no longer distinguish the boundaries of the colors, so they are merged. ³ An example given by Livingstone, (Vision and Art, 2002), shows a tightly packed array of non-overlapping blue and yellow pigment dots, which, from a distance appears gray. White would be the result if blue and yellow lights were used, but the example is reflective and, as the researcher explains, the

130 luminosity is lower.

The size of colored dots in an array, with respect to the size of receptor fields of the retina, must certainly be part of the retina's interpretation of the overall color of the array, but the role of the lens and pupil in focusing the diffusion may also be important. An array of tightly-packed colored

135 dots sheds more light than an array of colored dots spaced on a black field. If the pupil contracts under the brighter condition, the amount of radiation entering the eye from any given point will be smaller and, though there are more dots in the tightly packed array, the smaller quantity of light from each point means there will be less color from any given dot.

140 An arrangement in which colored dots are spaced on a black field should, according to the theory, evoke stronger signals from the ganglion cells (and certain other intervening cells). In addition, under such darker conditions the total reflectance decreases and the pupil may dilate. In this case, a larger quantity of radiation from any given colored point will be selected by the aperture and there will be more energy from each dot. If the latter is true, then colors seem stronger on dark

145 grounds, because there is more color stimuli. (The increase in energy through a dilated aperture depends on the nature of the light source. If a source is but one small radiating point, the increase will fall off at a rate according to the tangent between the radius of the aperture and the diverging angles of light quanta departing the source (plus the increased time required for this light to traverse the longer hypotenuse). But if the source is an array of diffusely reflecting dots covering

150 an area larger than the aperture, then the directions of reflections are numerous and much of the light quanta converges toward the opening. The energy increase will be more or less rectilinear (the area of the dilated aperture miiius the area of the contracted aperture)).

Livingstone (Vision and Art, 2002), references numerous artists in her assessment of pointillist

155 color, and Rosotti, (Colour, 1983, p 136-7), writes "...optical mixing need not yield only white; a mosaic of red and green gives a vibrant yellow. Such effects have been much exploited in textile design..." Though textile designers and artists may have employed additive color-mixing, either consciously or unconsciously, the author has not found three-dimensional implementations] similar to. the Type I varieties outlined in this specification.

160

Color-coding is often used to clarify geometric structures, both three-dimensional and two dimen¬ sional, and frequently appears in text-books and computer simulations. Their intention, however, is not to generate new color. As well, many color models employ three virtual dimensions for simplifying the representation of colors, and are particularly useful as interfaces for computer

165 users. These color-space models vary both the hue intensity, (or saturation), and the light/dark values by positioning the primaries, plus white and black, at different points in virtual 3-D. A 3-D matrix is convenient since the primaries and their ratios can be represented as one plane repeated as a stack of planes extending along a third axis between black and white. Two dimensional slices from the stack are then consulted and a point on the slice is specified.

170

There is also a product called Color-Cube, (patent no. 05634795, Davies, 1997), which seeks to show in 3-dimensions, the virtual color-space as an array of smaller real cubes, each small cube being painted with a unique color matched to one of the numerous emissive selections. The intention of the Color Cube, however, is not to actually mix colors additively.

175

Transparent colored polyhedra, such as decorative containers, are not uncommon. For a polyhedron with transparent additive-color faces (RGB), the faces will function subtractively and absorb color from distal faces. These cancellations of color weaken the result in the same way stirring additive primaries does. With transparent subtractive colored faces (magenta, yellow, and cyan),

180 the faces of the polyhedra will also function subtractively, but to a positive effect. A cyan face (cyan stimulates our blue and green receptors) will absorb, or filter, the red from a yellow face behind it (yellow stimulates our red and green receptors). The perceived color will be the bright yellow-green of the additive system.

185 Background for Type II Kinetic Color Generators

A yellow-orange can be perceived from a rapid succession of red and green paint swatches, (as on a spinning disk). This is a purely additive process because the two colors are coming to the eye unfiltered and at different times — the pigments have no opportunity to cancel each other. Newton

190 used spinning discs sectioned in various colors to determine the seven primaries of his system, and one can still buy a Newton color wheel from any number of educational-instrument outlets. Spinning color discs like this work by rapid sequencing of color through two dimensions, which is similar to a convergence of light from a static arrangement of points, but one that takes advantage of the cone receptors response time.

195

In the literature are found suggestions of using rotational means to make secondary color from pairs of red, green, or blue. There are science projects instructing students to color half a disc in one primary and the other half in another primary to arrive at a single secondary color, but they operate by rotation through only two dimensions, and do not incorporate all three primaries with

200 a dark, or zero-light function. Furthermore, descriptions of reflected-light additive-primary color wheel experiments such as these, at least those found by this author, do not accurately describe the primaries, (i.e. range of wavelengths or nature of pigments), so it is difficult to determine the quality of the complements produced.

205 There is an antique pump-action top still in production that uses three, geared, tricolor discs to effect changing secondary colors, but, as many old toys, the primaries are red, yellow, and blue with the red and blue of hues associated with the subtractive primaries, not the additive primaries. It is an interesting device, and utilizes a black field for part of its effect, but the use of subtractive primaries for optical mixing is the reason why it is not as effective as the one outlined in this

210 application. (The device doesn't make a vibrant green and can be improved by using additive primaries). There is another spinning color device, (US patent #2631405) that in principle sounds similar to the one presented here, but, like the previous example, it employs mostly subtractive primaries for an additive process. Its structure also limits the coloration schemes along one axis. None of the above operate by means of the example representing Type fl ^* , which expresses the

215 Process by shadows (dark intervals) interacting with the three RGB primaries on a rotating tilted plane, sometimes in precession. In terms of mechanics, the most relevant item is the flip-over top (01780547, Alland, 1930, and an improvement, British patent 656540, Christie and Jay Ltd., 1951). The kinetic aspect, the mechanics unrelated to the color, of the top represented in Type II of the application, may also be a simple model for strong Stark and Zeeman effects in which electron orbits are displaced from

220 their nuclei by magnetic or electric fields.

What optical mechanism may be responsible for the intense secondary colors in the shadows cast by the shaft of the top presented here, which are surrounded by lighter areas and should produce the opposite effect (less color against lighter grounds), is not known to the applicant, but it would seem to be related

225 to direction-sensitive amacrine cells. There may also be some color after-image effects enhancing the secondary color produced by the flashes of the two primaries from the disc.

Background for Type III, the Kinematic Color Generators

230 The Kinematic Color Generators employ a simple graphic system which permits the Process to be expressed in a strictly two dimensional rotation without creating a whitish or greyish blur of all three RGB primaries. Since it is easy to apply this system onto discs (or three-dimensional surfaces), traditional spinning tops might be one of the simplest manifestations.

235 Most spinning tops create concentric blurs of their stationary images because they rotate at thousands of revolutions per minute. The image discernible in their stationary phases is no longer discernible while rotating and any new concentric pattern formed while rotating shows no clear organization of color or new color. There is a tendency is to fill the entire visible area with many colors and the spinning effects are usually a let down. To avoid this dull result, pigments are

240 frequently applied to tops as concentric circles, but once spinning there is no change — the color in any given circumference is the same in both phases. A pattern of colors, where circles are composed of two colors will produce blurred combinations of colors, but the stationary image is already circular. A staggered pattern where colors also occupy neighboring circumferences, such as rings of interleaved elements, is also essentially circular in both phases. Furthermore, the additive

245 color process is not taken into account. The graphic system of Type III resolves the problem by translates the Process as elliptical openwork structures (some of them resembling atoms as commonly symbolized), to produce in the rotating phase discernible multi-colored concentric rings (some resembling atomic spectra).

250 There are perhaps billions of spinning tops in the world, and perhaps billions with colors. To search them all is impossible. However, the novelty of the Kinematic Color Generators suggests to the applicant that if this system were already known, it would continue to be exploited, and by probability alone, he would have seen an example by now. He has not.

255 Background Summary

The prior art seems to differ from applications of the Process in the following ways:

The known kinetic devices rotating in two-dimensions are, a) reflective with subtractive-primaries; 260 b) reflective with additive-primaries but without dark function, c) emissive but do not employ the emissive or transmissive equivalents of the graphic systems in Type III.

The known static devices are, a) diffusely reflective employing to some degree RGB primaries and dark elements but are two dimensional, b) three-dimensional but do not employ additive primaries, 265 c) three-dimensional with additive primaries but not reflected under incidental white light.

The following true/false table lays out the differences of which the applicant is aware.

270 category diflυse reflec¬ RGB dark color change of prior art tion under primaries function effected by white light reorientation textiles T T T F paintings T T possible F

275

3-D T T F F rotational T T F F top-like T F T T electronic F T T T

Process T T T T

280

Other references include U.S. patent no. 02184125, Patterson, 1939; U.S. patent no. 03474546, Wedlake, 1969; U.S. patent no. 05310183, Glikman, 1994; U.S. patent no. 05634795, Davies, 1997; U.S. patent no. 06050566, Shameson, 1998; U.S. patent no. 02583275, Olson, 1949; U.S. 285 patent no. 02332507, Dailey, 1943; U.S. patent no. 00547764, Boyum, 1895; and the work of artists Lucas Samaras, and Sol Le Witt, and Ellsworth Kelly.

¹ Dowling, The Retina, 1987; Livingstone, Vision and Art, 2002; Gergenfurtener and Sharpe, Color Vision, 1999; see chapter 7 of Dowling for general information on dark adaptation and cellular 290 dark-responses.

² Livingstone, Vision and Art, 2002 ³ ibid.

BRIEF DESCRIPTION OF THE INVENTION:

295

The invention underlies a set of three-dimensional art objects which may also find utility in the studies of vision science, geometry and physics. In all cases (except for emissive and transparent variants mentioned in the last paragraph of section I, titled Type I Openwork Color Generator) the apparent luminance of reflected colors is altered by the introduction of zero (or low) light intervals.

300 In Type I, the intervals of darkness lie between colored regions in a static manner. In the Type H, the intervals of darkness are integrated between rapid successions of colored regions. In Type III, the intervals of darkness are also integrated between rapid successions of colored regions but the domains of the primaries are first configured like that of Type I. When viewed under incidental white light, the objects exhibit additive primaries by diffuse reflection to stimulate sensations of

305 secondary colors — magenta, cyan, and yellow — and tertiary colors. Again, the primaries exhibited from these objects are those primary colors associated with the additive system, (namely blue, green, red), but are diffusely-reflective, not illuminants. The objects may be viewed together or independently. The primaries, blue, green, and red, labelled B, G, or R in the figures and text, are detailed at the end of the specification.

310

BRIEF DESCRIPTION OF THE DRAWINGS

FIG 1 shows one manifestation of the invention described in the first subsection titled 'Type I, Openwork Color Generator'.

315 FIG 2 shows a third manifestation of the invention described in the first subsection as an 'openwork white generator'.

FIG 3 shows the structure of two small versions of the invention described in the first subsection titled

'Type I, Openwork Color Generator'.

FIG 4 shows the first view of Type II of the invention, a spinning top, described in the II subsection 320 titled 'Kinetic Color Generator.' This figure shows the parts and general proportion of the top.

FIG 5 shows a sectional view of the spinning top illustrated in FIG.4 and the inclination produced by the addition of one weight [4].

FIGS 6 through 9 show views of the spinning top illustrated in FIG.4 as it proceeds through one period of rotation. 325 FIG 10 shows an alternate design for the spinning top of Type II illustrated in FIG 4.

FIG 11 relates to Type III generators and shows rosettes composed of a unit ellipse repeated about the focus, each rosette exhibiting one primary of either red [R], green [G], or blue [B]. In FIG. 11 , ellipses of each rosette has one of its foci in common.

FIG. 12 also relates to Type III ellipses. The nested rosettes of ellipses each rosette being either red 330 [R], green [G], or blue [B], are centered on their axes of symmetry.

FIG 13 Elemental ellipses, in either red [R], green [G], or blue [B], of a thicker ellipse are fanned out, each at 36°.

FIG. 14 shows single ellipses, red [R], green [G], or blue [B].

FIG. 15 shows another variety where the lines are cut short by the edge of the disc, and 345 FIG 16 shows a simulation of what the Type III generator of FIG 15 color bands look like when spinning

FIGS 17 and 18 show lattices described in the text of section III.

340 DETAILED DESCRIPTION OF THE INVENTION

I. Type I Openwork Color Generator

As stated above, Type I is nearly static and employs color-mixing by means of diffusely-reflected 355 RGB stimuli converging on the retina. Ratios of these primaries stimulating sensations of second¬ ary and tertiary colors are created by overlapping domains — for secondary colors these are in pairs — of red (R) green (G) or blue (B) elements comprising openwork structures against black backgrounds under incidental white light. Changes in the ratios of these stimuli are controlled by changes in orientation of the overlapping domains of R, G, or B, with respect to an observer. 350 Parallax between anterior and posterior regions of a three-dimensional openwork structure is a natural occurrence for an observer in motion with respect to the structure and is an easy method of effecting this change.

The following is an example: An arrangement of a set of sheets made from openwork material, 355 such as but not limited to wirecloth, is pigmented so that one of each of the RGB 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 1/3 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

360 the arrangement. For instance if the cube in FIG 2 were increased in the y dimension, the colors occupying the faces extended in y might also increase. For variations where clarity is unimportant, neither the ratios of R, G, or B domains need restriction to 1/3, 1/3, 1/3, nor does the structure supporting the R, G, or B domains need any particularly clear form.

365 ' The sheets are arranged so that an observer will see pairs of sheets superposed and pairs from the group of the primaries at virtually 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, other axial joints, pegs, fusing the material, knotting, twisting, bending, screws, etc.

370

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 environment 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

375 angles help to eliminate shadows. (In this case shadows are an unintentional interference).

At varying distances and angles, an observer is prompted 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 380 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 FIG 1 and with the primaries

385 arranged with each primary assigned to two whole faces (both inside and out), 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's plane approaches 0°. The increased density of this colored light passes through the open regions of the colored face nearest the viewer, which is 90° to the former. This allows for different ratios of the two

390 primaries. The varying ratios of two different primaries produce variants of the secondary colors. If the arrangement forms a hexahedron with each primary assigned to two whole faces, there are five possibilities for positioning the colors. 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.

395

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's apertures are proportionally small with respect to its 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

400 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 FlG 1, however the openwork may be inconsistent to produce variations of the color generating effects.

405 The distance required for the seeing the secondary colors is relative to the scale of the elements comprising the color domains, as can be assumed by what is already known about poinitllistic color. However it may be of interest to note that in this Process one can determine secondary color even though the primaries have so much space between them, which helps to verify the 'low resolution' of color perception. If the RGB elements are from .5mm to lmm with about 5mm space between them,

410 overlapping domains narrow the space to about 2.5 mm (and less when the screens are at angles). At 3 meters from the eye, when the angles of green and red domains are acute the perception of yellow can be nearly that of a solid swatch of yellow pigment. The perception of cyan and magenta seems to occur at shorter distances and after looking at the object for a period of time, one's eye tends to recognize the secondaries even at close range.

415

Constructions like those pictured in FIG 3, where arrangements are reduced to unit elements, produce limited color results because effectiveness partly depends on the quantity of units — the number of overlaps increases the number of retinal color responses. Also, if the arrangement is such that pairs of the primary-colored domains are not separated by an adequate distance from the third primary,

420 then tinted tertiary mixtures of all three primaries begin to arise, which when all three are in equal proportions, creates white.

Many forms with a single sheet are also possible — torus, hyperpoloid, sphere, cone, and highly com¬ plex forms. Since the domains of RGB can be located anywhere on a sheet, clarity, or meaningfulness

425 in the placement of color is the only concern for these constructions. Can the Process help clarify certain features? Or because of the changing color from different angles, will it cause confusion? A cylinder with open ends is shown in FIG 2 but instead of three primaries it reflects only one additive primary (blue, green, or red) and its secondary complement (yellow, magenta, or cyan), each color assigned to one lengthwise half of the cylinder. These produce white against a black

430 ground — openwork white generators.

Derivatives of the openwork generators might include lattices of emissive light. Three RGB primaries of laser light can be reflected along a mirrored framework to reflect their light in a vapor or gas cloud. Technically, phosphorescent and fluorescent pigments (or dyes), which re-emit

435 invisible ultraviolet light as longer visible wavelengths, are considered emissive sources, but they do not require connected power sources like lasers or neon. Results with fluorescent pigments are hindered by the pinkish nature to all the 'reds' and upon viewing one does not get a sense of a complete spectrum, but flourescents do form a bridge between the strictly reflective and the strictly emissive, operate under both incidental white light and 'blacklight', and are not uninteresting.

440

The lattices can be applied as opaque inks or paint to a clear substrate such as plate glass, but there are inherent problems of reflections from the glass, and the flatness of printed elements requires illumination from many angles. While not as effective, but still pleasing, a hybrid of the additive and subtractive color-mixing processes is created by substituting opaque reflective additive-

445 primaries (RGB) with transparent additive-primaries (RGB) on a transparent support There exists some absorption or cancellation of color when the transmitted primaries from distant domains are filtered through the pigments' nearest domains. Since the structure is open, this absorption is limited only to the colored elements and there remains a substantial additive color-mixing component But since the background will be white (transparent color against black is black), the contrast weakens the

450 additive-color (ganglion cells respond weakly when their entire fields are stimulated).

11. Kinetic Color Generator

The spinning top illustrated in FIG 5 has a rigid disc [2] fixed between the spheroid base [1] and the

455 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'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

460 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 FIG

465 4 may be increased or decreased slightly. The general proportions to obtain the desired motion can be inferred from the dimensions provided here, which assumes a solid hardwood base [1] of 31.75mm diameter by 23.8125 mm height, a disk [2] of similar solid material (such as basswood ply) in the range of 47.5mm to 54mm in diameter by 1.6 to 2 mm thick, and a shaft [3] of similar solid material with a length ranging from about 25mm to 32mm, with diameter 6.35mm.

470

FIG 5 shows one clip weight [4] applied to the disc, and the center of mass shifted slightly from a location [Ml] above the base's radial center [Q], to a point [M2] 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 [M2] in such way as to create, at various locations in the sweep of the top's motion, different

475 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].

FIGS 6 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

480 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's sweep, a lower region of color occurring toward

485 the front of the disc's sweep, two colored regions in the shadows cast on the disc by the shaft, and two colored regions on the shaft itself. The regions of secondary colors related to the shaft and its shadows, are indicated in italics [Y] and [AfJ. The two regions of color at the disc's upper and lower extremes are not referenced in the figures but can be inferred by examining the disc's orientation across the horizontal dimension and summing the occurrence of primary colors, (the figures are

490 aligned horizontally along the focus of the cycle). In FIGS 6 through 9, the colors would be cyan in the disc'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.

495

Variations in the degree of inclination, the period, or periods, between maximal and minimal inclina¬ tion, 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, (.00065 grams per cubic millimeter), tends to

500 either change angle and color in regular intervals , or stabilize at a constant angle until a disturbance interrupts it. In the latter case, when there is no disturbance and the top is not also spinning around its own axis of symmetry it does not exhibit precession and therefore exhibits no shifts in the observed secondary colors. Similar color effects occur if a saddle shaped disc is fitted to a standard conical point and shaft, but there is no precessional change in this variety FIG 9. The arc of the base

505 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 (.00118 grams per cubic millimeter), can be balanced to produce a progressive precession which gradually falls to about 30°, 510 or even 40° from vertical.

The top should be spun under adequate illumination and while not consequential to the effectiveness of the device, spinning on a dark surface enhances one's perception of the colors. To best see the colors, the top should be spun very fast. Ideally the tops might be made of a plastic with the same

515 density of the hardwood, providing consistency in manufacturing, but the irregularities of wood make each one slightly unique. Based on the dynamics outlined above one can forsee many superficial design modifications. As an alternative to the repositionable clip [4], and the means used in the original flip-over tops, there are numerous other ways to shift weight. A bit of wax or bubble gum can be placed under the disc or it may become more cost effective to make three tops, each

520 weighted differently, some with slightly elliptical discs, some with notches or holes, or holes all the way around, one or two being plugged, or a loop of string or elastic with a knot or bead. The top can be spun with a launcher.

III. Type HI, Kinematic Color Generator

525

As previously stated in the Background, Type III is a synthesis of Types I and II, and is character¬ ized by rapid movement of RGB openwork structures or openwork graphics. In Type III, the chromatic change is modulated by rotating a static system of lines or points of RGB through two dimensions. The integration of black occurs beyond the colored elements through the spaces

530 between them, as in Type I, or located adjacent to, and moving with, the colored elements.

Flattened varieties of Type III

The three-dimensions of Type I can be flattened if there is reasonable means to apportion the 535 primaries into ratios other than 1 : 1 : 1. A two-dimensional surface rotating in the very same two dimensions affords no other direction for apportioning the color domains but radially inward or outward, otherwise all three colors will end up in the same arc of rotation and be a grayish white. One can apportion the colors like a pie as Newton did but the whole disc will generate the same color.

540 This generator has a visible two-dimensional surface capable of rotation about an axis 90° to the surface's extension in those dimensions and does not involve precession or change in angle as part of its operation. Instead, ellipses observed when viewing a circular disc in precession or in the motion of the top described in part II, have been translated as nested rosettes of linear ellipses fixed to the plane of a disk (or platform suitable for spinning). The rosettes may vary according to the focus, shape,

545 size, line-widths of ellipses, and the number of unit ellipses per rosette. The lines of each rosette intersect according to the number of repetitions of the unit ellipse per arc and the difference in length between the unit ellipse's major and minor vertices.

While rosettes of ellipses (and similar geometric figures, including those with straight lines) are 550 certainly not new, they may be original as expressed here with diffusely-reflective RGB primaries over black grounds — in some of the nested rosettes described here, secondary colors begin to appear in the stationary phase at short distances because the lines are very thin. This however, may not qualify as functionally distinct beyond the prior art and remains a two dimensional relative of the Type I. 555

When the Type III generators are spun, however, concentric bands of new colors appear as line- widths of the ellipses are summed through the arcs of rotation. The resulting quantity of color per concentric band is the sum of all the colored ellipse line-widths cut by the arc. The thickness of a uniform line-width with respect to the arc of rotation, increases with curvature of the ellipse. This 560 system of ellipses in rotation against a dark field provides a way to include all three primaries on one surface and generate surprisingly clean unambiguous secondary colors and an extremely wide range of tertiary colors.

Not illustrated are these permutations: a) the system of nested ellipses as described above where each 565 ellipse itself is divided into red, green, and blue segments, b) the same system of ellipses as described above where the ellipses are not solid lines but dotted lines. The same system of ellipses can be applied emissively by lighting additive primaries from behind, or even with LEDs (but if the disc is in the form of a spinning top, in the dark one can't see the top itself).

570 Many of the ellipse patterns can also be extrapolated as single lines representing the traced path of a point in an elliptical orbit which itself is in rotation. For the example in FIG 13, the single line would be divided into three sections of the three primaries red green and blue.

The substrate of the surface [5] upon which the colored ellipses appear can be either opaque 575 or clear. A black field [K] as indicated in illustration 11 through 18, is made to surround the colored ellipses. When the substrate is clear, the device can be spun in front differently colored grounds, or black or white, each of which effects the nature of the perceived colors on the spinning surface. Unlike the kinetic color generator, the elliptic generators can also be augmented with other primaries from the subtractive set, but the surprise upon spinning is diminished. The primaries on 580 transparent subtrates may be transparent (filters) and from the subtractive set. But again, the more colors applied, the more the difference between stationary and rotating phases shrinks.

Some of the rosettes suggest a two-dimensional simile of an atom's electron's orbit as conceived by Rutherford and Bohr in the early days of atomic theory — the stationary phase being similar to the

585 elliptic orbits, and the spinning stage similar to an atom's spectral signature.

Also pictured are lattices of opaque red, green, and blue dots. The grids of opaque additive- primaries cover a transparent disc, or are surrounded by a field of black pigment. Experiments with other shapes of grid elements were also tested. 590

Three-dimensional varieties of Type III

Many of the above Type III graphics can be used on the top entitled Kinetic Color Generator as described in section II, (including the saddle shape variety). All of the above kinds of ellipse patterns 595 can be extrapolated in three dimensions as a stack of wire or die-cut rosettes. The two-dimensional projections can also be translated as a wire, or string of material extending, like a spring, into the axis of rotation.

600 IV Conclusion, Best Mode Contemplated and Personal Insertion

As one can see, there are numerous possibilities of the Process. From works of art, to color studies, educational devices and candy shelf novelties.

605 I feel I have already described some of the best modes. I have contemplated and tested hundreds of possibilities of the Type IH and have begun to explore their three-dimensional extensions. The Type IU will work well as gyroscopes, but hubcaps? As for other possibilities, large photographic halftones might be composed of differently-sized beads. Each primary would be separated such that at certain viewing angles, coinciding images produce near complete color representations. But this would be a

610 lot of work, and to reverse four-color scanning technology to arrive at the necessary separations to know where to put all those opaque RGB beads might require more insanity than even I am willing to risk. Why not just use transparent CMYK glass beads? Of course there is a different sensation between transparent media and the opaque. So simple beaded lattices in sheets, or strung to occupy a volume, might be better. In a room lull of rods dangling out of empty blackness, from one vantage

615 point a viewer would see a volume of red rods, blue rods, and green rods — whiteness. From another angle the viewer might see pairs and other combinations. Spheres with thousands of long radians or curving tentacles, each sphere a different RGB primary, can be interleaved. A helix can be colored with the three primaries running lengthwise, inside and out With its central axis in a circle forming a torus, it too can be balanced and rotated. Geodesic balls could collect dust on a shelf or in a comer.

620 Pencil holders which wouldn't be effective when full. Would sugar cube lattices on a black display, or candy-tops, entice children to learn a little more about color and photoreceptors? Since few adults could explain it either, one has to wonder if this would be a good mode. Would they really read the brochure?

625 V. Appendix

Wavelengths of the reflected primaries

The additive primary red [R] indicated in this specification and the figures reflects wavelengths

570-650 ntn with peak values near 620 nm. The additive primary green [G] indicated in this

630 specification and the figures reflects wavelengths 500-650 nm and slight reflection toward the 400 nm range, 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 440nm. An alternative blue [B] reflects wavelengths 400-700 nm with two peak values, one near 440nm and the second near 510 (there is a third curve at the very far end of the red near 700 but hard to

635 notice with the naked eye).

Pigments and pigment compounds used for the invention

The primary pigment compounds can be made from a number of fundamental coloring agents. The author has obtained them using the following pigments: Ultramarine blue (PB 29); Cobalt blue (PB

645 28); Cadmium reds; Cadmium orange; Cadmium yellow; Napthol 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. Fluorescent pigments were tested in 2003 but with lesser quality paints and the results were poor. They may have contained too much fluorescent white. But this can be remedied with better quality inks and paints or by adjusting the

650 pigment load. Fluorescents are, to a degree, emissive, but because they are also diffusely reflective under incidental white light they help complete the continuity between purely reflective additive processes decribed here and the purely emissive.

Pigment compounds for Blue 655 Ultramarine is exceedingly dark at full strength and needs some white added to bring the reflectance within range of the other two colors. Tinted ultramarine reflects wavelengths in a curve which peaks at about the same frequency as the absorption curve for the retinal receptor of blue light, which is about 425 nm.

660 Pigment compounds for Green

Phthalocyanine green, a very bluish green, reflecting wavelengths in a curve that peaks at about 500 nm but stretches into the retina's green receptor range, can be mixed with yellow pigment to cancel the blue and leave most of the mixture in range of the green photoreceptor, which peaks at 530 nm. The desired green is a very yellow green similar to the color seen when looking up

665 through a canopy of sunlit vegetation. Arylide yellow reflects wavelengths in a flat topped curve from 500 to 700 nm, which includes 530 and 560 nm where the absorption curves for two retinal photoreceptors peak for green and red, respectively. Reflecting only green and blue, the phthalo, absorbing most everything above 550 nm, absorbs the red of the arylide. Reflecting only red and green and absorbing everything below 500, the arylide absorbs all the blue of the phthalo. We are

670 left with a green compound reflecting wavelengths in the green photoreceptor's range.

Pigment compounds for Red

Napthol red, which should be a very warm red, can be applied straight. The retinal photoreceptor for the red light wavelength has a peak absorption rate at about 560 nm, and the bottom range 675 of napthol is about 560 nm.

Alteration of values

Aside from needing to be as bright and intense as possible, the values of all three primaries indicated above can be changed to some degree but it is important the relationship between values

680 remains somewhat consonant. The blue pigments, in all cases of the specified invention have been modified with white, such that on a value scale from 1 to 10 where red is near 6, green near 5, then blue is near 4. Likewise, if the red and green are near 6 and 7, then the blue is near 5.

685

690

695

700

705

710

715

800