Patterns - Gödel, Escher, Bach

Pattern is an orderly arrangement of things forming a consistent or characteristic arrangement or sequence. While in two dimensional art we can produce patterns comprised of repeated shapes or modules, a pattern can also be any regular rhythm in time or space. Patterns can also be used to create identical shapes or parts. 

Pattern-makers--from dress-design to boat manufacture--are highly valued for their conceptual and design abilities. Patterns pervade nature. People and plants grow in patterns, and so do spirals and money in the bank. Pendulums move in patterns, as do waves and spinning tops and springs. Sailors are on the lookout for patterns of sea and sky and wind that tell of bad weather. Parents look for behavior patterns in children that spell different kinds of turbulence ahead. Economists look for patterns of spending and saving. 

Patterns are essential to perception because if we could not pick out patterns among the sound vibrations we heard or the light vibrations we saw, all the world would be a buzzing white confusion. All animals--and probably plants--have built-in pattern perceivers as part of their innate biological structure. Indeed, pattern perception or pattern recognition is important to the survival of every organism. Our ability to perceive the most subtle of patterns helps us to navigate and understand the world in which we live. Consider the patterns of clouds; the ways in which water moves; the tracks animals leave; the irregular beating of a heart or the "sticky valve" of a car engine. Each "orderly arrangement of things" allows us to perceive something different about our world. 

Sometimes the patterns we employ to perceive the world filter out other less familiar patterns, and make us literally blind to new ways of seeing and thinking. Patterns extend our perceptions and also obscure them. A pattern implies that something happens over and over again. It can help you find out where you're going, and where you've been; what's happening now, and what's going to happen next. It can be a sequence of things, a mutual force, a relationship in time or space. If one thing follows another in a repeatable way, you may think they are related by cause and effect. When two patterns collide or intersect they often create an "interference pattern" such as a moirepattern in which two patterns produce a third "wave-like" pattern. Texture can be understood as simply pattern that is better appreciated with fingers rather than the eyes; textures are really just very small repeated patterns. Very fine patterns or textures feel smooth to the touch. Subtle differences between textures may only be discernible through the sense of touch. Coarser textures may be readily perceived by the eyes--for example, corduroy fabric or the surface of a rasp. When creating a composition that requires intermediary tones, visual texture--such as cross-hatched lines or rubbings (frottage)--can be used to provide interest and richness to a visual field. 

TOOLS FOR THINKING 
isomorphism, PARADOX, RECURSION, INFINITY FORMAL SYSTEMS 

ARTISTS / CULTURAL REFERENCES 
 African textiles, Amish Quilts, Crystallography, M.C. Escher, Fractals, Islamic architecture, Agnes Martin, Bridget Riley, Victor Vasareley, Navajo Weaving, Robert Zakanitch 

FURTHER READING ON PATTERNING: 
Briggs, John and David Peat, Turbulent Mirror, Harper and Row, 1989. 

Mandelbrot, Benoit B., The Fractal Geometry of Nature, 1977. 

Miller, Mary, "The Practical Fractal,"Exploring Magazine, Vol. 16, No.2, Summer 1992. 

Morrison, Phylis & Philip, "Crystalligraphy," Exploring Magazine, Vol. 16, No.2, Summer 1992. 

Stevens, Peter S., Handbook of Regular Patterns, The MIT Press, 1980. 

Zaslavsky, Claudia, "Symmetry along with other Mathematical Concepts and Applications in African Life,"Applications in School Mathematics (Yearbook, National Council of Teachers of Mathematics, Sidney Sharron and Robert Reys, eds.), 1979. 

Harris, Mary, "Symmetry and Dissymmetry in Mathematics Education: a View from England," Leonardo, Vol. 23, 1990. (A challenging feminist look at symmetries, using 'women's works' as examples.)