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A pattern is a regularity in the world, in human-made design, or in abstract ideas. As such, the elements of a pattern repeat in a predictable manner. A geometric pattern is a kind of pattern formed of geometric
shape A shape or figure is a graphical representation of an object or its external boundary, outline, or external surface, as opposed to other properties such as color, texture, or material type. A plane shape or plane figure is constrained to lie ...
s and typically repeated like a
wallpaper Wallpaper is a material used in interior decoration to decorate the interior walls of domestic and public buildings. It is usually sold in rolls and is applied onto a wall using wallpaper paste. Wallpapers can come plain as "lining paper" (so ...
design. Any of the senses may directly observe patterns. Conversely, abstract patterns in science, 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 Patterns in nature are visible regularities of form found in the natural world. These patterns recur in different contexts and can sometimes be modelled mathematically. Natural patterns include symmetries, trees, spirals, meanders, waves, f ...
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 CW4Kid ...
, rarely exactly repeating, and often involve fractals. Natural patterns include
spirals In mathematics, a spiral is a curve which emanates from a point, moving farther away as it revolves around the point. Helices Two major definitions of "spiral" in the American Heritage Dictionary are:meanders, waves,
foam Foams are materials formed by trapping pockets of gas in a liquid or solid. A bath sponge and the head on a glass of beer are examples of foams. In most foams, the volume of gas is large, with thin films of liquid or solid separating the r ...
s, tilings, cracks, and those created by
symmetries Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definiti ...
of rotation and reflection. Patterns have an underlying 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
visual motifs The visual system comprises the sensory organ (the eye) and parts of the central nervous system (the retina containing photoreceptor cells, the optic nerve, the optic tract and the visual cortex) which gives organisms the sense of sight (the a ...
may be combined and repeated to form patterns designed to have a chosen effect on the viewer. In computer science, a
software design pattern In software engineering, a software design pattern is a general, reusable solution to a commonly occurring problem within a given context in software design. It is not a finished design that can be transformed directly into source or machine co ...
is a known solution to a class of problems in programming. In fashion, the pattern is a
template Template may refer to: Tools * Die (manufacturing), used to cut or shape material * Mold, in a molding process * Stencil, a pattern or overlay used in graphic arts (drawing, painting, etc.) and sewing to replicate letters, shapes or designs ...
used to create any number of similar garments. In many areas of the
decorative arts ] The decorative arts are arts or crafts whose object is the design and manufacture of objects that are both beautiful and functional. It includes most of the arts making objects for the interiors of buildings, and interior design, but not usua ...
, from ceramics and textiles to
wallpaper Wallpaper is a material used in interior decoration to decorate the interior walls of domestic and public buildings. It is usually sold in rolls and is applied onto a wall using wallpaper paste. Wallpapers can come plain as "lining paper" (so ...
, "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 In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as il ...
dimension,
spirals In mathematics, a spiral is a curve which emanates from a point, moving farther away as it revolves around the point. Helices Two major definitions of "spiral" in the American Heritage Dictionary are:meanders, waves,
foam Foams are materials formed by trapping pockets of gas in a liquid or solid. A bath sponge and the head on a glass of beer are examples of foams. In most foams, the volume of gas is large, with thin films of liquid or solid separating the r ...
s, tilings, cracks and stripes.


Symmetry

Symmetry is widespread in living things. Animals that move usually have bilateral or 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 Starfish or sea stars are star-shaped echinoderms belonging to the class Asteroidea (). Common usage frequently finds these names being also applied to ophiuroids, which are correctly referred to as brittle stars or basket stars. Starfish ...
, sea urchins, and sea lilies. 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. Crystals have a highly specific set of possible crystal symmetries; they can be cubic or
octahedral In geometry, an octahedron (plural: octahedra, octahedrons) is a polyhedron with eight faces. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at ea ...
, but cannot have fivefold symmetry (unlike quasicrystals).


Spirals

Spiral patterns are found in the body plans of animals including
molluscs Mollusca is the second-largest phylum of invertebrate animals after the Arthropoda, the members of which are known as molluscs or mollusks (). Around 85,000 extant species of molluscs are recognized. The number of fossil species is estim ...
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 The common sunflower (''Helianthus annuus'') is a large annual forb of the genus ''Helianthus'' grown as a crop for its edible oily seeds. Apart from cooking oil production, it is also used as livestock forage (as a meal or a silage plant), as ...
and fruit structures like the pineapple.


Chaos, turbulence, meanders and complexity

Chaos theory Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to have ...
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
oscillate Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum ...
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

Foam Foams are materials formed by trapping pockets of gas in a liquid or solid. A bath sponge and the head on a glass of beer are examples of foams. In most foams, the volume of gas is large, with thin films of liquid or solid separating the r ...
s obey
Plateau's laws Plateau's laws describe the structure of soap films. These laws were formulated in the 19th century by the Belgian physicist Joseph Plateau from his experimental observations. Many patterns in nature are based on foams obeying these laws. 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
radiolarian The Radiolaria, also called Radiozoa, are protozoa of diameter 0.1–0.2 mm that produce intricate mineral skeletons, typically with a central capsule dividing the cell into the inner and outer portions of endoplasm and ectoplasm. The ela ...
s,
sponge Sponges, the members of the phylum Porifera (; meaning 'pore bearer'), are a basal animal clade as a sister of the diploblasts. They are multicellular organisms that have bodies full of pores and channels allowing water to circulate through ...
spicule Spicules are any of various small needle-like anatomical structures occurring in organisms Spicule may also refer to: *Spicule (sponge), small skeletal elements of sea sponges * Spicule (nematode), reproductive structures found in male nematodes ...
s, and the skeletons of
silicoflagellate Dictyochales (Silicoflagellates, or Dictyochophyceae ''sensu stricto'') are a small group of unicellular heterokont algae, found in marine environments. Characteristics In one stage of their life cycle, they produce a siliceous skeleton, comp ...
s and sea urchins.


Cracks

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 Alan Mathison Turing (; 23 June 1912 – 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher, and theoretical biologist. Turing was highly influential in the development of theoretical co ...
, 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 pattern Spatiotemporal patterns are patterns that occur in a wide range of natural phenoma and are characterized by a spatial and a temporal patterning. The general rules of pattern formation hold. In contrast to "static", pure spatial patterns, the ...
s 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
tiling Tiling may refer to: *The physical act of laying tiles *Tessellations Computing *The compiler optimization of loop tiling * Tiled rendering, the process of subdividing an image by regular grid *Tiling window manager People * Heinrich Sylvester T ...
or
carpet A carpet is a textile floor covering typically consisting of an upper layer of pile attached to a backing. The pile was traditionally made from wool, but since the 20th century synthetic fibers such as polypropylene, nylon, or polyester hav ...
, 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, 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
column A column or pillar in architecture and structural engineering is a structural element that transmits, through compression, the weight of the structure above to other structural elements below. In other words, a column is a compression member. ...
s, 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 In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as il ...
-like way at different sizes. See also:
pattern book A pattern book, or architectural pattern book, is a book of architectural designs, usually providing enough for non-architects to build structures that are copies or significant derivatives of major architect-designed works. A number of pattern boo ...
.


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 Patterns in nature are visible regularities of form found in the natural world. These patterns recur in different contexts and can sometimes be modelled mathematically. Natural patterns include symmetries, trees, spirals, meanders, waves, f ...
including the mathematics of symmetry, waves, meanders, and fractals.
Fractal In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as il ...
s 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
formation Formation may refer to: Linguistics * Back-formation, the process of creating a new lexeme by removing or affixes * Word formation, the creation of a new word by adding affixes Mathematics and science * Cave formation or speleothem, a secondar ...
can be simple (e.g.
Lindenmayer system An L-system or Lindenmayer system is a parallel rewriting system and a type of formal grammar. An L-system consists of an alphabet of symbols that can be used to make strings, a collection of production rules that expand each symbol into some ...
s 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 software engineering, a software design pattern is a general, reusable solution to a commonly occurring problem within a given context in software design. It is not a finished design that can be transformed directly into source or machine co ...
, in the sense of a
template Template may refer to: Tools * Die (manufacturing), used to cut or shape material * Mold, in a molding process * Stencil, a pattern or overlay used in graphic arts (drawing, painting, etc.) and sewing to replicate letters, shapes or designs ...
, 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
template Template may refer to: Tools * Die (manufacturing), used to cut or shape material * Mold, in a molding process * Stencil, a pattern or overlay used in graphic arts (drawing, painting, etc.) and sewing to replicate letters, shapes or designs ...
, 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 The concept of an archetype (; ) appears in areas relating to behavior, historical psychology, and literary analysis. An archetype can be any of the following: # a statement, pattern of behavior, prototype, "first" form, or a main model that ot ...
*
Cellular automata A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessel ...
*
Form constant A form constant is one of several geometric patterns which are recurringly observed during hypnagogia, hallucinations and altered states of consciousness. History In 1926, Heinrich Klüver systematically studied the effects of mescaline (peyote ...
*
Fractal In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as il ...
*
Pattern (sewing) In sewing and fashion design, a pattern is the template from which the parts of a garment are traced onto woven or knitted fabrics before being cut out and assembled. Patterns are usually made of paper, and are sometimes made of sturdier materi ...
*
Pattern coin A pattern coin is a coin which has not been approved for release, but produced to evaluate a proposed coin design. They are often off-metal strike (using metals of lower value to test out the dies), to proof standard or piedforts. Many coin col ...
* Pattern matching *
Pattern recognition Pattern recognition is the automated recognition of patterns and regularities in data. It has applications in statistical data analysis, signal processing, image analysis, information retrieval, bioinformatics, data compression, computer grap ...
* Pattern (casting) *
Patterns in nature Patterns in nature are visible regularities of form found in the natural world. These patterns recur in different contexts and can sometimes be modelled mathematically. Natural patterns include symmetries, trees, spirals, meanders, waves, f ...
*
Pedagogical patterns A pedagogical pattern is the re-usable form of a solution to a problem or task in pedagogy, analogous to how a design pattern is the re-usable form of a solution to a design problem. Pedagogical patterns are used to document and share best practices ...


References


Bibliography


In nature

* Adam, John A. ''Mathematics in Nature: Modeling Patterns in the Natural World''. Princeton, 2006. * Ball, Philip ''The Self-made Tapestry: Pattern Formation in Nature''. Oxford, 2001. * Edmaier, Bernhard ''Patterns of the Earth''. Phaidon Press, 2007. * Haeckel, Ernst '' Art Forms of Nature''. Dover, 1974. * Stevens, Peter S. ''Patterns in Nature''. Penguin, 1974. * Stewart, Ian. ''What Shape is a Snowflake? Magical Numbers in Nature''. Weidenfeld & Nicolson, 2001. * Thompson, D'Arcy W.
On Growth and Form
'. 1942 2nd ed. (1st ed., 1917).


In art and architecture

* 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 * Concepts in epistemology Concepts in metaphysics Concepts in the philosophy of mind Concepts in the philosophy of science Design