Pattern
Natural patterns include spirals, meanders, waves, foams, tilings, cracks, and those created by symmetries of rotation and reflection.
In many areas of the decorative arts, from ceramics and textiles to wallpaper, "pattern" is used for an ornamental design that is manufactured, perhaps for many different shapes of object.
In art and architecture, decorations or visual motifs may be combined and repeated to form patterns designed to have a chosen effect on the viewer.
Nature provides examples of many kinds of pattern, including symmetries, trees and other structures with a fractal dimension, spirals, meanders, waves, foams, tilings, cracks and stripes.
[2]: 48–49 Plants often have radial or rotational symmetry, as do many flowers, as well as animals which are largely static as adults, such as sea anemones.
[2]: 64–65 Among non-living things, snowflakes have striking sixfold symmetry: each flake is unique, its structure recording the varying conditions during its crystallisation similarly on each of its six arms.
[6] Many natural patterns are shaped by this complexity, including vortex streets,[7] other effects of turbulent flow such as meanders in rivers.
[11] Foams obey Plateau's laws, which require films to be smooth and continuous, and to have a constant average curvature.
Foam and bubble patterns occur widely in nature, for example in radiolarians, sponge spicules, and the skeletons of silicoflagellates and sea urchins.
Cracking patterns are widespread in nature, for example in rocks, mud, tree bark and the glazes of old paintings and ceramics.
[14] Alan Turing,[15] and later the mathematical biologist James D. Murray[16] and other scientists, described a mechanism that spontaneously creates spotted or striped patterns, for example in the skin of mammals or the plumage of birds: a reaction–diffusion system involving two counter-acting chemical mechanisms, one that activates and one that inhibits a development, such as of dark pigment in the skin.
[17] These spatiotemporal patterns slowly drift, the animals' appearance changing imperceptibly as Turing predicted.
[20] Repetitions need not be identical; for example, temples in South India have a roughly pyramidal form, where elements of the pattern repeat in a fractal-like way at different sizes.
Previous work has demonstrated consistent trends in preference for and complexity estimates of fractal patterns.
