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A pattern is a regularity in the world, in human-made design, or in
Symmetry is widespread in living things. Animals that move usually have bilateral or Reflection symmetry, mirror symmetry as this favours movement. 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. Fivefold symmetry is found in the echinoderms, including starfish, sea urchins, and sea lilies.
Among non-living things, snowflakes have striking dihedral symmetry, sixfold symmetry: each flake is unique, its structure recording the varying conditions during its crystallisation similarly on each of its six arms. Crystals have a highly specific set of possible crystal habit, crystal symmetries; they can be cubic or octahedral, but cannot have fivefold symmetry (unlike quasicrystals).
Spiral patterns are found in the body plans of animals including molluscs such as the nautilus, and in the phyllotaxis of many plants, both of leaves spiralling around stems, and in the multiple spirals found in flowerheads such as the sunflower and fruit structures like the pineapple.
Chaos theory predicts that while the laws of physics are deterministic, there are events and patterns in nature that never exactly repeat because extremely small differences in starting conditions can lead to widely differing outcomes. The patterns in nature tend to be static due to dissipation on the emergence process, but when there is interplay between injection of energy and dissipation there can arise a complex dynamic. Many natural patterns are shaped by this complexity, including vortex streets, other effects of turbulent flow such as meanders in rivers. or nonlinear interaction of the system
Waves are disturbances that carry energy as they move. Mechanical waves propagate through a medium – air or water, making it Oscillation, oscillate as they pass by. Wind waves are surface waves that create the chaotic patterns of the sea. As they pass over sand, such waves create patterns of ripples; similarly, as the wind passes over sand, it creates patterns of dunes.
Foams obey Plateau's laws, which require films to be smooth and continuous, and to have a constant mean curvature, average curvature. Foam and bubble patterns occur widely in nature, for example in radiolarians, sponge spicule (sponge), spicules, and the skeletons of silicoflagellates and sea urchins.
Fracture, Cracks form in materials to relieve stress: with 120 degree joints in elastic materials, but at 90 degrees in inelastic materials. Thus the pattern of cracks indicates whether the material is elastic or not. Cracking patterns are widespread in nature, for example in rocks, mud, tree bark and the glazes of old paintings and ceramics.
Alan Turing, and later the mathematical biologist James D. Murray 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.Ball, Philip. ''Shapes''. 2009. Pages 159–167. These spatiotemporal patterns slowly drift, the animals' appearance changing imperceptibly as Turing predicted.
See also: pattern book.
Mathematics is sometimes called the "Science of Pattern", in the sense of rules that can be applied wherever needed. For example, any sequence of numbers that may be modeled by a mathematical function can be considered a pattern. Mathematics can be taught as a collection of patterns.
On Growth and Form
'. 1942 2nd ed. (1st ed., 1917).
abstract
Abstract may refer to:
* ''Abstract'' (album), 1962 album by Joe Harriott
* Abstract of title a summary of the documents affecting title to parcel of land
* Abstract (law), a summary of a legal document
* Abstract (summary), in academic publishi ...
ideas. As such, the elements of a pattern repeat in a predictable manner. A geometric pattern is a kind of pattern formed of geometric
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ca ...
shapes and typically repeated like a wallpaper design.
Any of the senses may directly observe patterns. Conversely, abstract patterns in science, mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
, or language may be observable only by analysis. Direct observation in practice means seeing visual patterns, which are widespread in nature and in art. Visual patterns in nature are often chaotic
Chaotic was originally a Danish trading card game. It expanded to an online game in America which then became a television program based on the game. The program was able to be seen on 4Kids TV (Fox affiliates, nationwide), Jetix, The CW4Kids ...
, rarely exactly repeating, and often involve fractals. Natural patterns include spirals, meanders, waves, foams, tilings, fracture, cracks, and those created by Symmetry, symmetries of rotation symmetry, rotation and reflection symmetry, reflection. Patterns have an underlying Mathematics, mathematical structure; indeed, mathematics can be seen as the search for regularities, and the output of any function is a mathematical pattern. Similarly in the sciences, theories explain and predict regularities in the world.
In art and architecture, decorations or Motif (visual arts), visual motifs may be combined and repeated to form patterns designed to have a chosen effect on the viewer. In computer science, a software design pattern is a known solution to a class of problems in programming. In fashion, the pattern is a Die (manufacturing), template used to create any number of similar garments.
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.
Nature
Nature provides examples of many kinds of pattern, including symmetry, symmetries, trees and other structures with a fractal dimension, spirals, meanders, waves, foams, tilings, fracture, cracks and stripes.Symmetry
Symmetry is widespread in living things. Animals that move usually have bilateral or Reflection symmetry, mirror symmetry as this favours movement. 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. Fivefold symmetry is found in the echinoderms, including starfish, sea urchins, and sea lilies.
Among non-living things, snowflakes have striking dihedral symmetry, sixfold symmetry: each flake is unique, its structure recording the varying conditions during its crystallisation similarly on each of its six arms. Crystals have a highly specific set of possible crystal habit, crystal symmetries; they can be cubic or octahedral, but cannot have fivefold symmetry (unlike quasicrystals).
Spirals
Spiral patterns are found in the body plans of animals including molluscs such as the nautilus, and in the phyllotaxis of many plants, both of leaves spiralling around stems, and in the multiple spirals found in flowerheads such as the sunflower and fruit structures like the pineapple.
Chaos, turbulence, meanders and complexity
Chaos theory predicts that while the laws of physics are deterministic, there are events and patterns in nature that never exactly repeat because extremely small differences in starting conditions can lead to widely differing outcomes. The patterns in nature tend to be static due to dissipation on the emergence process, but when there is interplay between injection of energy and dissipation there can arise a complex dynamic. Many natural patterns are shaped by this complexity, including vortex streets, other effects of turbulent flow such as meanders in rivers. or nonlinear interaction of the system
Waves, dunes
Waves are disturbances that carry energy as they move. Mechanical waves propagate through a medium – air or water, making it Oscillation, oscillate as they pass by. Wind waves are surface waves that create the chaotic patterns of the sea. As they pass over sand, such waves create patterns of ripples; similarly, as the wind passes over sand, it creates patterns of dunes.
Bubbles, foam
Foams obey Plateau's laws, which require films to be smooth and continuous, and to have a constant mean curvature, average curvature. Foam and bubble patterns occur widely in nature, for example in radiolarians, sponge spicule (sponge), spicules, and the skeletons of silicoflagellates and sea urchins.
Cracks
Fracture, Cracks form in materials to relieve stress: with 120 degree joints in elastic materials, but at 90 degrees in inelastic materials. Thus the pattern of cracks indicates whether the material is elastic or not. Cracking patterns are widespread in nature, for example in rocks, mud, tree bark and the glazes of old paintings and ceramics.
Spots, stripes
Alan Turing, and later the mathematical biologist James D. Murray 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.Ball, Philip. ''Shapes''. 2009. Pages 159–167. These spatiotemporal patterns slowly drift, the animals' appearance changing imperceptibly as Turing predicted.
Art and architecture
Tilings
In visual art, pattern consists in regularity which in some way "organizes surfaces or structures in a consistent, regular manner." At its simplest, a pattern in art may be a geometric or other repeating shape in a painting, drawing, tapestry, ceramic Tile, tiling or carpet, but a pattern need not necessarily repeat exactly as long as it provides some form or organizing "skeleton" in the artwork. In mathematics, a tessellation is the tiling of a plane using one or more geometric shapes (which mathematicians call tiles), with no overlaps and no gaps.In architecture
In architecture, Motif (visual arts), motifs are repeated in various ways to form patterns. Most simply, structures such as windows can be repeated horizontally and vertically (see leading picture). Architects can use and repeat decorative and structural elements such as columns, pediments, and lintels. 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.
See also: pattern book.
Science and mathematics
Mathematics is sometimes called the "Science of Pattern", in the sense of rules that can be applied wherever needed. For example, any sequence of numbers that may be modeled by a mathematical function can be considered a pattern. Mathematics can be taught as a collection of patterns.
Fractals
Some mathematical rule-patterns can be visualised, and among these are those that explain patterns in nature including the mathematics of symmetry, waves, meanders, and fractals. Fractals are mathematical patterns that are scale invariant. This means that the shape of the pattern does not depend on how closely you look at it. Self-similarity is found in fractals. Examples of natural fractals are coast lines and tree shapes, which repeat their shape regardless of what magnification you view at. While self-similar patterns can appear indefinitely complex, the rules needed to describe or produce their pattern formation, formation can be simple (e.g. Lindenmayer systems describing tree shapes). In pattern theory, devised by Ulf Grenander, mathematicians attempt to describe the world in terms of patterns. The goal is to lay out the world in a more computationally friendly manner. In the broadest sense, any regularity that can be explained by a scientific theory is a pattern. As in mathematics, science can be taught as a set of patterns.Computer science
In computer science, a software design pattern, in the sense of a Template method pattern, template, is a general solution to a problem in programming. A design pattern provides a reusable architectural outline that may speed the development of many computer programs.Fashion
In fashion, the pattern is a Die (manufacturing), template, a technical two-dimensional tool used to create any number of identical garments. It can be considered as a means of translating from the drawing to the real garment.See also
* Archetype * Cellular automata * Form constant * Fractal * Pattern (sewing) * Pattern coin * Pattern matching * Pattern recognition * Pattern (casting) * Patterns in nature * Pedagogical patternsReferences
Bibliography
In nature
* Adam, John A. ''Mathematics in Nature: Modeling Patterns in the Natural World''. Princeton, 2006. * Philip Ball, Ball, Philip ''The Self-made Tapestry: Pattern Formation in Nature''. Oxford, 2001. * Bernhard Edmaier, Edmaier, Bernhard ''Patterns of the Earth''. Phaidon Press, 2007. * Ernst Haeckel, Haeckel, Ernst ''Art Forms of Nature''. Dover, 1974. * Stevens, Peter S. ''Patterns in Nature''. Penguin, 1974. * Ian Stewart (mathematician), Stewart, Ian. ''What Shape is a Snowflake? Magical Numbers in Nature''. Weidenfeld & Nicolson, 2001. * D'Arcy Wentworth Thompson, Thompson, D'Arcy W.On Growth and Form
'. 1942 2nd ed. (1st ed., 1917).
In art and architecture
* Christopher Alexander, Alexander, C. ''A Pattern Language: Towns, Buildings, Construction''. Oxford, 1977. * de Baeck, P. ''Patterns''. Booqs, 2009. * Garcia, M. ''The Patterns of Architecture''. Wiley, 2009. * Kiely, O. ''Pattern''. Conran Octopus, 2010. * Pritchard, S. ''V&A Pattern: The Fifties''. V&A Publishing, 2009.In science and mathematics
* Adam, J. A. ''Mathematics in Nature: Modeling Patterns in the Natural World''. Princeton, 2006. * Resnik, M. D. ''Mathematics as a Science of Patterns''. Oxford, 1999.In computing
* Gamma, E., Helm, R., Johnson, R., Vlissides, J. ''Design Patterns''. Addison-Wesley, 1994. * Bishop, C. M. ''Pattern Recognition and Machine Learning''. Springer, 2007. {{metaphysics Patterns, * Concepts in epistemology Concepts in metaphysics Concepts in the philosophy of mind Concepts in the philosophy of science Design