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 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 ...
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 Stimulus (physiology), stimuli. (For example, in the human body, the brain which is part of the cen ...
s may directly observe patterns. Conversely, abstract patterns in
science
Science is a systematic endeavor that builds and organizes knowledge in the form of testable explanations and predictions about the universe.
Science may be as old as the human species, and some of the earliest archeological evidence for ...
,
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, waves, ...
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
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 of a river or other watercourse. It is produced as a watercourse erodes the sediments of an outer, concave bank ( cut bank) and deposits sediments on an inner, convex bank ...]
s,
wave
In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (res ...
s,
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 ...
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
Rotation, or spin, is the circular movement of an object around a '' central axis''. A two-dimensional rotating object has only one possible central axis and can rotate in either a clockwise or counterclockwise direction. A three-dimensional ...
and
reflection Reflection or reflexion may refer to:
Science and technology
* Reflection (physics), a common wave phenomenon
** Specular reflection, reflection from a smooth surface
*** Mirror image, a reflection in a mirror or in water
** Signal reflection, in ...
. 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
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 (th ...
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 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 ...
, "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 illu ...
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 of a river or other watercourse. It is produced as a watercourse erodes the sediments of an outer, concave bank ( cut bank) and deposits sediments on an inner, convex bank ...]
s,
wave
In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (res ...
s,
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 ...
s,
tilings,
cracks and stripes.
Symmetry
![Schnee1](https://upload.wikimedia.org/wikipedia/commons/3/3a/Schnee1.jpg)
Symmetry is widespread in living things. Animals that move usually have bilateral or
mirror symmetry
In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry.
In 2D ther ...
as this favours movement.
Plants often have radial or
rotational 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 anemones. Fivefold symmetry is found in the
echinoderms, including
starfish,
sea urchin
Sea urchins () are 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 shells (tests) of ...
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, macro ...
s 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 a ...
, but cannot have fivefold symmetry (unlike
quasicrystals
A quasiperiodic crystal, or quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry. While crystals, according to the classical ...
).
Spirals
![Aloe polyphylla spiral](https://upload.wikimedia.org/wikipedia/commons/c/c4/Aloe_polyphylla_spiral.jpg)
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
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 ...
, 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 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
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 centuri ...
.
Chaos, turbulence, meanders and complexity
Chaos theory predicts that while the laws of
physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
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 street
In fluid dynamics, a vortex ( : 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 in th ...
s, other effects of turbulent flow such as
meander
A meander is one of a series of regular sinuous curves in the channel of a river or other watercourse. It is produced as a watercourse erodes the sediments of an outer, concave bank ( cut bank) and deposits sediments on an inner, convex bank ...
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 equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (res ...
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 medium. While waves can move over long distances, the movement of the medium of transmission—the material—is limited. Therefor ...
s 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 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, f ...
s.
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 ...
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 elab ...
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 t ...
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 urchin
Sea urchins () are 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 shells (tests) of ...
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 co ...
,
and later the mathematical biologist
James D. Murray
James Dickson Murray FRSE FRS, (born 2 January 1931) is professor emeritus of applied mathematics at University of Washington and University of Oxford. He is best known for his authoritative and extensive work entitled '' Mathematical Biology' ...
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
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 ...
,
drawing
Drawing is a form of 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, crayons, ...
,
tapestry
Tapestry is a form of textile art, traditionally woven by hand on a loom. Tapestry is weft-faced weaving, in which all the warp threads are hidden in the completed work, unlike most woven textiles, where both the warp and the weft threads ma ...
, 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
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 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,
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 pedimen ...
s, and
lintel
A lintel or lintol is a type of beam (a horizontal structural element) that spans openings such as portals, doors, windows and fireplaces. It can be a decorative architectural element, or a combined ornamented structural item. In the case of w ...
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 illu ...
-like way at different sizes.
![Evening columns Zeus temple Athens](https://upload.wikimedia.org/wikipedia/commons/7/75/Evening_columns_Zeus_temple_Athens.jpg)
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
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 objects in which repetitions are allowed and order matters. Like a set, it contains members (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is calle ...
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, ...
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 illu ...
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 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, are statistically se ...
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 so ...
s describing
tree
In botany, a tree is a perennial plant with an elongated stem, or trunk, usually supporting branches and leaves. In some usages, the definition of a tree may be narrower, including only woody plants with secondary growth, plants that are ...
shapes).
In
pattern theory, devised by
Ulf Grenander
Ulf Grenander (23 July 1923 – 12 May 2016) was a Swedish statistician and professor of applied mathematics at Brown University.
His early research was in probability theory, stochastic processes, time series analysis, and statistical theory (p ...
, 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 ...
*
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 illu ...
*
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 mate ...
*
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
In computer science, pattern matching is the act of checking a given sequence of tokens for the presence of the constituents of some pattern. In contrast to pattern recognition, the match usually has to be exact: "either it will or will not be ...
*
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 graphi ...
*
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, waves, ...
*
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
(known in English as ''Art Forms in Nature'') is a book of lithographic and halftone prints by German biologist Ernst Haeckel.
...
''. 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