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      After the paint floating in the pan is has been manipulated into a design, paper treated with an alum solution is lowered onto the surface. When the paper is picked up, most of the paint adheres to it, since it is chemically more attractive to the paint than is the liquid bath. 

      I used much of this beautiful paper to make paper polyhedra. I love crystals. When I was doing macramé in 1970, a large hanging composed entirely of knots in cotton cord, I saw how different knots aggregated into different shapes, for instance, a helix. I realized that it was similar to the way the various crystal shapes develop depending on their differently-shaped atoms.

      I wish I had the skills to grow wonderful crystals. I have learned to mimic crystallization by hand by engraving a 2-D design of closely-spaced lines onto Plexiglas using a rotary power tool, lines which catch the light. I also apply paint to the Plexiglas and carve through it. Lit from behind, my works gleam like stained glass.

      I gravitated to this new medium after dyes in my batiks and shiboris faded. Pigments are far more colorfast than dyes, and will stick to Plexiglas if it is sanded to give it “tooth” to hold the paint. The paint needs an additive. I use Golden liquid acrylic paints diluted with liquid acrylic medium and GAC 200, an additive for inflexible surfaces. I select pigments that are translucent. Opaque black gives me the drama of complete darkness, and the exposed plastic, created with lines engraved through the paint layer, gives me something brighter than white—a great dynamic range.

Figure 8 An Essential Mystery: Life Creates,
acrylic paint on 1/8” Plexiglas with engraved lines: 45 in. diameter circle.

      In An Essential Mystery: Number Governs Form, the circle represents a geode, with amethyst crystals pointing inward. At the center is a much-enlarged Scotch thistle blossom. With both subjects, I used actual specimens to guide my work. The thistle disintegrated into thistledown.

      Amethyst is a type of quartz, whose crystal form is hexagonal in cross section, with six equal rectangular faces. In nature, of course, slight misalignments of atoms in the crystal lattice are commonplace. I took great pleasure in studying the actual specimens and trying to capture their regularity-with-variety. Engraving the lines with a power rotary tool enhanced the crystalline effect. As I mentioned, the plastic had been sanded to accept the paint, making it look frosty. When one looks head-on through a quartz crystal, it is quite transparent, but less so when looking at the oblique faces. My quartz-crystal illusion was greatly enhanced when I polished the plastic on certain areas to restore transparency.

      Crystal forms are determined by the atomic properties of their elements. Crystals grow not only in ways determined by the shape of their atoms, like Lego toy pieces, but are constrained by the binding forces between atoms. Some elements like carbon take different forms, diamond and graphite, depending on the binding forces.

      When it comes to living things, relatively recent investigations in the physical sciences show that pattern-generating processes, ones that develop through time in an excitable medium, may play a role in generating som biological patterns. Belousov’s 1951 experiments with oscillating chemical reactions, ones that spontaneously produced spirals and target shapes in motion (the BZ reaction), touched off a new line of inquiry, as did a 1952 paper by Alan Turing on morphogenesis that suggested hypothetical chemical reactions giving rise to patterns of stripes and spots. In biology, these relate to “a fibrillating heart’s pulses, the stripes on leopards, and more...all bear a resemblance to oscillating chemical reactions as well as other patterns called Turing patterns that develop through time.”[15] The oscillations are kept going by an interplay between chemicals that activate or inhibit.

      The new light this throws on evolutionary theory is worth exploring in some detail. When we say an “eye” pattern forms on a moth’s wing because it serves to scare away predators, what kind of explanation is that? How could variations of shuffled genes through dim recesses of time have turned up that particular card? But experiments with oscillating reactions produce similar patterns! DNA code for a simple pattern-generating recipe using the very nature of the materials at hand is straightforward. Natural selection then favors the particular “eye” configuration. There is no “DNA map of a scary eye” as such.

Philip Ball, in The Self-Made Tapestry, elaborates on recent, sometimes controversial, research:
     " [T]hese processes suggest that there are certain ‘fundamental’ structures of organisms that are not at all determined by the arbitrary experimentation and weeding out that evolution is thought to involve. Instead, these structures have an inevitability about them, being driven by the basic physics and chemistry of growth. If life were started from scratch a thousand times over, it would every time alight on these fundamental structures eventually. Within the parlance of modern physics, they are attractors—stable forms or patterns to which a system is drawn regardless of where it starts from....[I]f the protagonists of this concept turn out to be validated, that would not by any means bring Darwin tumbling from his pedestal. There is absolutely no question that natural selection operates in the real world and that it has produced the tremendous variety of organisms with which we share the planet....No one argues, meanwhile, that nature’s palette is not constrained by the rules of physics and chemistry. If the formation of patterns by symmetry-breaking proves to pose limitations of evolutionary choices, that will add just one more nuance to Darwin’s towering achievement."[16]

      I painted Number Governs Form in 1993. I would later learn of Brian Goodwin’s work (How the Leopard Changed its Spots: The Evolution of Complexity, 1994) and Philip Ball’s book, 1999. However, it was already well known that the thistle is the product of a recursive growth process that produces thorns on the flower at regular intervals that fit the Fibonacci series of numbers. These numbers are also found in measurements relating to the “Golden Rectangle” of geometry.

      As well, the Fibonacci numerical patterns observed in a sunflower spiral and elsewhere are associated with a “Golden Angle” of 137.5æ, the angle at which a succession of sunflower seeds form or leaves are offset in a spiral along a growing stem.[17] The sunflower spiral can be replicated by an experiment with magnetic droplets that repel each other.

      For a plant to place the next seed or leaf, it need not “know” the correct angle: The dynamics of growth cause it to keep “discovering” it.[18] Experiments are being done with plant hormones to explain the stop-and-start process of stem development that gives rise to these relationships. The hormones inhibit leaf development as the stem grows. When the stem is longer, hormone concentration diminishes, and leaf development resumes. Now, to discover the peculiar mathematical relationships that develop!

      The Fibonacci spiral is a rich template for generating designs. Recently, I used several permutations of it to convey an idea that has held me in its grip since 1975, that “all knowledge is one.” In 1990, E.O. Wilson wrote Consilience, which shows the connections he sees between all branches of knowledge.[19] Therefore, I have named my fourth and most recent version of this piece, completed in 2004, A Vast Consilience

Figure 10 A Vast Consilience, 2004, acrylic on Plexiglas, engraved lines: 48 in. square