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".

ABSTRACT
      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.[1] 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." [2]

      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.”[3] 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.”[4] 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.[5]

      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.[6]

      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[7] 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.
 


Figure 3 Animal, Vegetable, Mineral, 1977, 18 batiks,each triangle 9 feet on a side.

      As well, I learned the joy of pattern-generating processes of tie-dye. Folding and binding fabric in a systematic way prevents dye from entering the folds. The result always surprises. Complex results can occur from quite simple manipulations.

      I like to draw. I was attracted to Japanese shibori (a tie dye variant), where one draws, say, a bamboo leaf, and stitches along the lines of the image with strong thread. It is gathered and secured, using the threads as drawstrings. The tightly-drawn folds are not very deep. Success demands the use of dyes like indigo that do not penetrate well, but remain on the surface of the bound-up cloth. Cutting the threads and ungathering the folds reveals the pattern. An exciting moment! The works had an appearance of not being handmade, but created by some natural process.

      When the cloth is tightly drawn up, ruffles in the cloth surrounding the design prevent it from dyeing evenly, creating a halo effect. Kirlian photographs capture a halo effect of natural specimens by placing them on an electrically-charged photographic plate in a dark room. One of my favorite Kirlian photographs was of a large leaf photographed by this process. The Kirlian Effect was my interpretation of it in shibori.


Figure 4 The Kirlian Effect, 1979,
shibori on cotton/polyester: 14 X 27 in


      Kirlian uses traditional shibori branching patterns writ large. I then demonstrated shibori could also be used for erosion patterns. My shibori technique demonstrated that the similarity between branching (a growth process) and erosion (a subtractive process) is pronounced, because both involve bifurcation. That is, at certain points in their development, the stem or the ridge becomes divided.

      How does the “erosion” pattern develop when sewn? Sometimes stitching follows the lines of a drawing, but another method is stitching perpendicular to the lines. Horizontal rows of stitches create vertical wrinkles that become the design. By offsetting the stitches, branching patterns begin to emerge (mokume shibori, or “wood grain”). Sewing a spiral path in the cloth gathers the wrinkles into something that looked to me like ridges of a deeply-eroded volcano. This is clearly seen in Seismic Fuji, (detail).


Figure 5 Seismic Fuji, detail, 1982,
shibori on cotton: 30 X 30 X 5 in.

      The shibori process proved too labor-intensive, but gave me a feeling for what wrinkles would naturally do. This intuition was utilized in my next series of landscapes that looked like satellite photos, dubbed my N.A.S.A. series (Not Actually Science Achievements). Combining what I knew about geology and shibori, I wrinkled thin vegetable paper into “mountainscape” reliefs. These were sprayed from several angles with different colors of spray paints. If water areas were called for, I protected the lowest areas of the relief with a resist of ordinary sand. Unlike the sewn shiboris, these were swiftly executed. The three-dimensionality and degree of detail seemed uncanny to viewers. I was able to mimic certain geologic formations. For instance, in Appalachian II one can see the typical pattern that sedimentary rocks make when uplifted by folding, then truncated by subsequent erosion.

      An 1989 article about my work in Kagaku Asahi,[8] a Japanese popular science magazine, raised an interesting question: Could the wrinkling process really be an analog to Earth’s features, which are largely caused by erosion? My hunch is that the answer is yes, because the forces that crumple and lift up the earth’s crust create weaknesses in the strata, guiding erosion by water or ice. David Huffman, a mathematician formerly at U.C. Santa Cruz, did an analysis of crumpled brown paper bags, measuring the angles of folds where they joined together. He found several relations that always hold true. For instance, when many folds meet at a point, there is always an even number of them. In such a group he would number each angle and found that the sum of the degrees of the odd-numbered angles equals that of the even-numbered ones.[9] The crumpling processes must have similarities ro geologic forces uplifting mountains, or it would not be so very easy to create my illusions! Manipulating actual material, paper, easily yielded results more realistic than the first computer-generated fractal landscapes.