The Study of Patterns is Profound
Published in Leonardo, Volume 40 Number 3, 2007, http://www.leonardo.info
Trudy Myrrh Reagan is an artist who founded YLEM: Artists Using Science and Technology in 1981. In 2004, she started an interest group within YLEM on the subject of patterns, both natural and mathematical. She paints under the name "Myrrh".
The author has studied natural patterns both by drawing them and finding analogs for them in crafts materials. Several media will be described: batik, shibori, wrinkled paper painting, paper marbling, constructing a moiré, and painting and engraving on Plexiglas. As well, she will discuss the generation of the patterns in nature, and how scientists’ understanding of them expanded during the period of her own explorations. She recommends this study for enhancing one’s connection to the natural world and the cosmos. The author also explains how she found patterns useful as metaphors for philosophic ideas.
The artist’s eye is captivated even from childhood by rainbow stripes on mud puddles or drifting smoke. The movement of smoke, for example, that mesmerized me when I was small came from my mother’s cigarets or embers in the campfire. Gazing at wisps of smoke is no trivial matter! Drifting up gracefully, smoke obeys laws of physics in a most visible way. It loses momentum and curls around in ever-changing patterns. Like smoke injected into wind tunnels for aeronautical research, it traces out air currents, in particular, the hot air rising from the cigaret. Cool air, which is denser, gently moves toward it to fill the partial vacuum it created. Where the smoke loses momentum, the warm and cool air circle around each other, hovering. The particles of smoke are supported by the invisible atmosphere, principally nitrogen and oxygen molecules. This is why I found an appealing logic in its apparent disorder.
For 45 years, I have explored comparable patterns in nature in my art. They turned out to be manifestations of profound truths, and a vehicle for expressing philosophic ideas as well.
My father, Philip B. King, illustrated his scientific papers and books with pen-and-ink drawings of crags and erosion patterns. He was well-known for his innovations in the means of visualizing sub-surface geology. I carry a memory of his office lined with colorful geologic maps. As well, I saw rainbow slide shows by his friend, projections of mineral thin sections under polarized light. Entering college in 1954 as a skilled representational artist, I was suddenly expected to generate abstract designs. I had scant facility for it. In my senior year, I discovered the just-published book, The New Landscape, by Gyorgy Kepes. In it, things I had seen all my life were honored as worthy art subjects, as much as the nonrepresentational art they resembled.
Nathan Cabot Hale, an art educator, wrote about the dilemma of the representational artist in our time:
"The biggest challenge to the artist today is learning the abstract language of art. Long ago it was enough to copy the surface forms of nature, but now it is our task to get at the root of nature’s meanings. There is no other way to do this than to learn the kind of reasoning that enables us to look beneath the surface of things." 
Leonardo did this with his famous sketches of turbulent water. Beginning in the 1880s, Odion Redon and others were inspired by the “landscapes” of cells under the microscope. The surface of the paintings of the cathedral doors at Rouen by Monet, 1904, have a fractal quality, though this was not even a concept or a word before Benoit Mandelbrot began mathematical work on fractals in the 1960s.
Mandelbrot dubbed fractals “the mathematics of wiggles.” They generated novel geometric designs, and when random numbers were added, computer artists found a tool to model nature. Peaks composed of random polygon shapes became “mountains.” However, geologists noted the lack of erosion patterns, and “behaviors” had to be integrated into to fractal algorithms.
One reason I love drawing is that it is an inexpensive way to “own” what I admire. My basic esthetic started with graceful lines in contour maps and patterns, both regular and chaotic, in geologic maps. From science magazine photographs, I mined an amazing array of designs possessing unusual line qualities. Imagine my delight in 1974 to see the patterns I enjoyed analyzed in Peter Stevens’ book, Patterns in Nature.
A 1970 experiment I did morphed one category of line quality into another around the circumference of the E Pluribus Unum skirt, from straight to contour-like to cellular and by stages back to straight lines.
Figure 1 E Pluribus Unum Skirt,
rayon skirt, 1969 (lost), recreated in 2005, 40 in. long
Several drawings I did in this period showed that patterns formed a family of motifs, ones that repeated at many scales. For instance, I did one of a gigantic leaf with "veins" of capillaries, street maps and so on:diverse, and yet so similar! Nature’s tendency toward conservation of energy generates similar forms, whether extremely large or extremely small.
Beginning in 1973, I learned batik and adopted hexagonal patterns as a theme in order to work in modules to create large wall pieces. Hexagons, with their 120¾ angles, tile a plane. Hexagons in nature are plentiful. I found many examples in Ernst Haeckle’s Art Forms in Nature and soon noticed them all around me. One morning I awoke on a camping trip and gazed into the branches of a Red Fir, which has perfect 30¾– 60¾ branching. The batik process added another natural-looking element. Batik is a process of drawing the design on thin fabric in wax, then dyeing it. The waxed areas resist the dye and remain white. Afterwards, the wax is removed from the cloth.
Figure 2 Red Fir, 12” X 15” detail of the batik, Animal, Vegetable, Mineral
During the dyeing process, the wax develops cracks, which the dye enters. This adds a pattern resembling a network of veins. In Red Fir, it resembles the needles of the conifer. This is part of a larger piece, Animal, Vegetable, Mineral.