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

On Growth and Form

'. 1942 2nd ed. (1st ed., 1917).

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 ...

shape
A shape or figure is a graphics, graphical representation of an object or its external boundary, outline, or external Surface (mathematics), surface, as opposed to other properties such as color, Surface texture, texture, or material type.
A pl ...

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 t ...

design.
Any of the sense
A sense is a biological system used by an organism for sensation, the process of gathering information about the world through the detection of stimuli. (For example, in the human body, the brain
A brain is an organ (biology), organ tha ...

s may directly observe patterns. Conversely, abstract patterns in science
Science is a systematic endeavor that Scientific method, builds and organizes knowledge in the form of Testability, testable explanations and predictions about the universe.
Science may be as old as the human species, and some of the earli ...

, 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
Language is a structured system of communication. The structure of a language is its grammar and the free components are its vocabulary. Languages are the primary means by which humans communicate, and may be conveyed through a variety of met ...

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, wav ...

are often chaotic, rarely exactly repeating, and often involve fractals
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 illus ...

. 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:meander
A meander is one of a series of regular sinuous curves in the Channel (geography), channel of a river or other watercourse. It is produced as a watercourse erosion, erodes the sediments of an outer, concave bank (cut bank) and deposits sedimen ...

s, wave
In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from List of types of equilibrium, equilibrium) of one or more quantities. Waves can be Periodic function, periodic, in which case those quantities ...

s, foam
Foams are materials science, materials formed by trapping pockets of gas in a liquid or solid.
A Sponge (tool), bath sponge and the Beer head, head on a glass of beer are examples of foams. In most foams, the volume of gas is large, with thin ...

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
Mathematics is an area of knowle ...

of rotation
Rotation, or spin, is the circular movement of an object around a ''axis of rotation, central axis''. A two-dimensional rotating object has only one possible central axis and can rotate in either a clockwise or counterclockwise direction. A t ...

and reflection. Patterns have an underlying mathematical
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 ...

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 may be combined and repeated to form patterns designed to have a chosen effect on the viewer. In computer science, a software design pattern
HTTP Switchboard, In software engineering, a software design pattern is a general, reusability, reusable solution to a commonly occurring problem within a given context in software design. It is not a finished design that can be transformed directl ...

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), molding process
* Stencil, a pattern or overlay used in graphic arts (drawing, painting, etc.) and sewing to replicate letters, sha ...

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 usual ...

, 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 t ...

, "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 afractal
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 illus ...

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:meander
A meander is one of a series of regular sinuous curves in the Channel (geography), channel of a river or other watercourse. It is produced as a watercourse erosion, erodes the sediments of an outer, concave bank (cut bank) and deposits sedimen ...

s, wave
In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from List of types of equilibrium, equilibrium) of one or more quantities. Waves can be Periodic function, periodic, in which case those quantities ...

s, foam
Foams are materials science, materials formed by trapping pockets of gas in a liquid or solid.
A Sponge (tool), bath sponge and the Beer head, head on a glass of beer are examples of foams. In most foams, the volume of gas is large, with thin ...

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 orrotational symmetry
Rotational symmetry, also known as radial symmetry in geometry, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which i ...

, as do many flowers, as well as animals which are largely static as adults, such as sea anemone
Sea anemones are a group of predation, predatory marine invertebrates of the order (biology), order Actiniaria. Because of their colourful appearance, they are named after the ''Anemone'', a terrestrial flowering plant. Sea anemones are classifi ...

s. Fivefold symmetry is found in the echinoderms
An echinoderm () is any member of the phylum Echinodermata (). The adults are recognisable by their (usually five-point) radial symmetry, and include starfish, brittle stars, sea urchins, sand dollars, and sea cucumbers, as well as the Crinoi ...

, including starfish
Starfish or sea stars are Star polygon, star-shaped echinoderms belonging to the class (biology), class Asteroidea (). Common usage frequently finds these names being also applied to brittle star, ophiuroids, which are correctly referred to ...

, sea urchin
Sea urchins () are spine (zoology), spiny, globular echinoderms in the class Echinoidea. About 950 species of sea urchin live on the seabed of every ocean and inhabit every depth zone from the intertidal seashore down to . The spherical, hard s ...

s, and sea lilies.
Among non-living things, snowflake
A snowflake is a single ice crystal that has achieved a sufficient size, and may have amalgamated with others, which falls through the Earth's atmosphere as snow.Knight, C.; Knight, N. (1973). Snow crystals. Scientific American, vol. 228, no. ...

s have striking sixfold symmetry: each flake is unique, its structure recording the varying conditions during its crystallisation similarly on each of its six arms. Crystal
A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macrosc ...

s have a highly specific set of possible crystal symmetries; they can be cubic or octahedral
In geometry
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 ...

, but cannot have fivefold symmetry (unlike quasicrystals).
Spirals

Spiral patterns are found in the body plans of animals includingmolluscs
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 taxon, extant species of molluscs are recognized. The number of fossil sp ...

such as the nautilus
The nautilus (, ) is a pelagic marine mollusc of the cephalopod family Nautilidae. The nautilus is the sole extant family of the superfamily Nautilaceae and of its smaller but near equal suborder, Nautilina.
It comprises six living species in t ...

, and in the phyllotaxis
In botany, phyllotaxis () or phyllotaxy is the arrangement of leaf, leaves on a plant stem. Phyllotactic spirals form a distinctive class of patterns in nature.
Leaf arrangement
The basic leaf#Arrangement on the stem, arrangements of leaves ...

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 plant, annual forb of the genus ''Helianthus'' grown as a crop for its Sunflower seed, edible oily seeds. Apart from sunflower oil, cooking oil production, it is also used as livestoc ...

and fruit structures like the pineapple
The pineapple (''Ananas comosus'') is a tropical plant with an edible fruit; it is the most economically significant plant in the family Bromeliaceae. The pineapple is indigenous to South America, where it has been cultivated for many centurie ...

.
Chaos, turbulence, meanders and complexity

Chaos theory
Chaos theory is an interdisciplinary area of scientific study and branch of 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 c ...

predicts that while the laws of physics
Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical science is that depar ...

are deterministic
Determinism is a Philosophy, philosophical view, where all events are determined completely by previously existing causes. Deterministic theories throughout the history of philosophy have developed from diverse and sometimes overlapping motive ...

, 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 street
In fluid dynamics, a vortex (plural, : vortices or vortexes) is a region in a fluid in which the flow revolves around an axis line, which may be straight or curved. Vortices form in stirred fluids, and may be observed in smoke rings, whirlpools ...

s, other effects of turbulent flow such as meander
A meander is one of a series of regular sinuous curves in the Channel (geography), channel of a river or other watercourse. It is produced as a watercourse erosion, erodes the sediments of an outer, concave bank (cut bank) and deposits sedimen ...

s in rivers. or nonlinear interaction of the system
Waves, dunes

Wave
In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from List of types of equilibrium, equilibrium) of one or more quantities. Waves can be Periodic function, periodic, in which case those quantities ...

s are disturbances that carry energy as they move. Mechanical wave
In physics, a mechanical wave is a wave that is an oscillation of matter, and therefore transfers energy through a transmission medium, medium. While waves can move over long distances, the movement of the medium of transmission—the material ...

s propagate through a medium – air or water, making it oscillate
Oscillation is the repetitive or Periodic function, periodic variation, typically in time, of some measure about a central value (often a point of Mechanical equilibrium, equilibrium) or between two or more different states. Familiar examples o ...

as they pass by. Wind wave
In fluid dynamics, a wind wave, water wave, or wind-generated water wave, is a surface wave that occurs on the free surface of Body of water, bodies of water as a result from the wind blowing over the water surface. The contact distance in the ...

s are surface wave
In physics, a surface wave is a mechanical wave that propagates along the Interface (chemistry), interface between differing media. A common example is gravity waves along the surface of liquids, such as ocean waves. Gravity waves can also occu ...

s 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 dune
A dune is a landform composed of wind- or water-driven sand. It typically takes the form of a mound, ridge, or hill. An area with dunes is called a dune system or a dune complex. A large dune complex is called a dune field, while broad, fl ...

s.
Bubbles, foam

Foam
Foams are materials science, materials formed by trapping pockets of gas in a liquid or solid.
A Sponge (tool), bath sponge and the Beer head, head on a glass of beer are examples of foams. In most foams, the volume of gas is large, with thin ...

s obey Plateau's laws
Plateau's laws describe the structure of soap films. These laws were formulated in the 19th century by the Belgium, Belgian physicist Joseph Plateau from his experimental observations. Many patterns in nature are based on foams obeying these 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 (biology), cell into the inner and outer portions of endoplasm and Ecto ...

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 organism, multicellular organisms that have bodies full of pores and channels allowing water ...

spicules, and the skeletons of silicoflagellates and sea urchin
Sea urchins () are spine (zoology), spiny, globular echinoderms in the class Echinoidea. About 950 species of sea urchin live on the seabed of every ocean and inhabit every depth zone from the intertidal seashore down to . The spherical, hard s ...

s.
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 ...

, 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 apainting
Painting is the practice of applying paint, pigment, color or other medium to a solid surface (called the "matrix" or "support"). The medium is commonly applied to the base with a brush, but other implements, such as knives, sponges, and ai ...

, drawing
Drawing is a form of Visual arts, visual art in which an artist uses instruments to mark paper or other two-dimensional surface. Drawing instruments include graphite pencils, pen and ink, various kinds of paints, inked brushes, colored pencils, ...

, tapestry
Tapestry is a form of textile arts, textile art, traditionally Weaving, woven by hand on a loom. Tapestry is weft-faced weaving, in which all the warp (weaving), warp threads are hidden in the completed work, unlike most woven textiles, where b ...

, ceramic tiling
Tiling may refer to:
*The physical act of laying tile
Tiles are usually thin, square or rectangular coverings manufactured from hard-wearing material such as ceramic, Rock (geology), stone, metal, baked clay, or even glass. They are generall ...

or carpet
A carpet is a textile floor covering typically consisting of an upper layer of Pile (textile), pile attached to a backing. The pile was traditionally made from wool, but since the 20th century synthetic fibers such as polypropylene, nylon, or ...

, 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
A tessellation or tiling is the covering of a surface, often a plane (mathematics), plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to high-dimensional ...

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 ascolumn
A column or pillar in architecture and structural engineering is a structural element that transmits, through compression (physical), compression, the weight of the structure above to other structural elements below. In other words, a column i ...

s, pediment
Pediments are gables, usually of a triangular shape.
Pediments are placed above the horizontal structure of the lintel, or entablature, if supported by columns. Pediments can contain an overdoor and are usually topped by hood moulds.
A pediment ...

s, and lintel
A lintel or lintol is a type of beam (a horizontal structural element) that spans openings such as Portal (architecture), portals, doors, windows and fireplaces. It can be a decorative architectural element, or a combined ornamented structural ...

s. 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 illus ...

-like way at different sizes.
See also: pattern book.
Science and mathematics

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 ...

is sometimes called the "Science of Pattern", in the sense of rules that can be applied wherever needed. For example, any sequence
In mathematics, a sequence is an enumerated collection of mathematical object, objects in which repetitions are allowed and order theory, order matters. Like a Set (mathematics), set, it contains Element (mathematics), members (also called ''eleme ...

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 explainpatterns 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, wav ...

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 illus ...

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
__NOTOC__
In mathematics, a self-similar object is exactly or approximately similarity (geometry), similar to a part of itself (i.e., the whole has the same shape as one or more of the parts). Many objects in the real world, such as coastlines ...

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 can be simple (e.g. Lindenmayer system
An L-system or Lindenmayer system is a wikt:parallel, parallel rewriting system and a type of formal grammar. An L-system consists of an alphabet of symbols that can be used to make string (computer science), strings, a collection of Production ...

s describing tree
In botany, a tree is a perennial plant with an elongated Plant stem, stem, or trunk (botany), trunk, usually supporting branches and leaves. In some usages, the definition of a tree may be narrower, including only woody plants with secondar ...

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, asoftware design pattern
HTTP Switchboard, In software engineering, a software design pattern is a general, reusability, reusable solution to a commonly occurring problem within a given context in software design. It is not a finished design that can be transformed directl ...

, in the sense of a template
Template may refer to:
Tools
* Die (manufacturing), used to cut or shape material
* Mold, in a molding (process), molding process
* Stencil, a pattern or overlay used in graphic arts (drawing, painting, etc.) and sewing to replicate letters, sha ...

, 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 atemplate
Template may refer to:
Tools
* Die (manufacturing), used to cut or shape material
* Mold, in a molding (process), molding process
* Stencil, a pattern or overlay used in graphic arts (drawing, painting, etc.) and sewing to replicate letters, sha ...

, 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, History of psychology#Emergence of German experimental psychology, historical psychology, and literary analysis.
An archetype can be any of the following:
# a statement, pat ...

* 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
* 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 illus ...

* Pattern (sewing)
In sewing and fashion design, a pattern is the stencil, template from which the parts of a garment are traced onto woven fabric, woven or knitted fabrics before being cut out and assembled. Patterns are usually made of paper, and are sometimes ...

* Pattern coin
* Pattern matching
In computer science, pattern matching is the act of checking a given sequence of Lexical analysis#Token, tokens for the presence of the constituents of some pattern. In contrast to pattern recognition, the match usually has to be exact: "either ...

* 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 ...

* Pattern (casting)
In casting, a pattern is a replica of the object to be cast, used to prepare the cavity into which molten material will be poured during the casting process.
Patterns used in sand casting may be made of wood, metal, plastics or other materials ...

* 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, wav ...

* Pedagogical patterns
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
Phaidon Press is a global publisher of books on art, architecture, design, fashion, photography, and popular culture, as well as cookbooks, Children's literature, children's books, and Travel literature, travel books. The company is based in Lon ...

, 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
Weidenfeld & Nicolson Ltd (established 1949), often shortened to W&N or Weidenfeld, is a British publisher of fiction and reference books. It has been a division of the French-owned Orion Publishing Group since 1991.
History
George Weidenfeld a ...

, 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