: 64–65Īmong 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. Fivefold symmetry is found in the echinoderms, including starfish, sea urchins, and sea lilies.

: 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. Animals that move usually have bilateral or mirror symmetry as this favours movement. 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. 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 fashion, the pattern is a template used to create any number of similar garments. In computer science, a software design pattern is a known solution to a class of problems in programming. 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. Similarly in the sciences, theories explain and predict regularities in the world. Patterns have an underlying mathematical structure : 6 indeed, mathematics can be seen as the search for regularities, and the output of any function is a mathematical pattern. Natural patterns include spirals, meanders, waves, foams, tilings, cracks, and those created by symmetries of rotation and reflection. Visual patterns in nature are often chaotic, rarely exactly repeating, and often involve fractals. Direct observation in practice means seeing visual patterns, which are widespread in nature and in art. Conversely, abstract patterns in science, mathematics, or language may be observable only by analysis. A geometric pattern is a kind of pattern formed of geometric shapes and typically repeated like a wallpaper design.Īny of the senses may directly observe patterns. As such, the elements of a pattern repeat in a predictable manner. A pattern is a regularity in the world, in human-made design, or in abstract ideas.

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