View source for Pattern

{{Short description|Regularity in sensory qualia or abstract ideas}}
{{Other uses}}
{{multiple image|perrow =2|total_width=450
| image1 = Ionic frieze from the Erechtheum, dimensions 130 x 50 cm, in the Glyptothek.jpg
| image2 = Kleophrades Painter ARV 189 78bis mission to Achilles.jpg
| image3 = William Morris - "Pimpernel" - Google Art Project.jpg
| image4 = Strawberrythief.jpg
| image5 = Settee MET SF2007 368 img4.jpg
| image6 = Nikoxenos Painter ARV 221 14 athletes with trainer and flute player - satyrs as athletes (05).jpg
| image7 = D.A. Sturdza House, Bucharest (Romania) 32.jpg
| footer = Various examples of patterns
}}

A '''pattern''' is a regularity in the world, in human-made design,<ref>{{cite web|url=https://www.achrafgarai.com/what-are-design-patterns/|title=What are design patterns?|website=achrafgarai.com|access-date=1 January 2023|first=Achraf|last=Garai|date=3 March 2022}}</ref> or in [[abstraction|abstract]] ideas. As such, the elements of a pattern repeat in a predictable manner. A '''geometric pattern''' is a kind of pattern formed of [[geometry|geometric]] [[shape]]s and typically repeated like a [[wallpaper]] design.

Any of the [[sense]]s 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]] are often [[Chaos theory|chaotic]], rarely exactly repeating, and often involve [[fractals]]. Natural patterns include [[spirals]], [[meander]]s, [[wave]]s, [[foam]]s, [[tessellation|tilings]], [[fracture|cracks]], and those created by [[Symmetry|symmetries]] of [[rotation symmetry|rotation]] and [[reflection symmetry|reflection]]. Patterns have an underlying [[Mathematics|mathematical]] structure;<ref name=":0">{{Cite book |last=Stewart |first=Ian |url=https://www.worldcat.org/oclc/50272461 |title=What shape is a snowflake? |date=2001 |publisher=Weidenfeld & Nicolson |isbn=0-297-60723-5 |location=London |pages= |oclc=50272461}}</ref>{{Rp|page=6}} 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 many areas of the [[decorative arts]], from ceramics and textiles to [[wallpaper]], "pattern" is used for an ornamental design that is manufactured, perhaps for many different shapes of object. In 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.

== Nature ==
{{main|Patterns in nature}}
Nature provides examples of many kinds of pattern, including [[symmetry|symmetries]], trees and other structures with a [[fractal]] dimension, [[spirals]], [[meander]]s, [[wave]]s, [[foam]]s, [[tessellation|tilings]], [[fracture|cracks]] and stripes.<ref>Stevens, Peter. ''Patterns in Nature'', 1974. Page 3.</ref>

=== Symmetry ===
[[File:First Snowfall (38115232341).jpg|thumb|upright|[[Snowflake]] [[dihedral symmetry|sixfold symmetry]]]]
Symmetry is widespread in living things. Animals that move usually have bilateral or [[Reflection symmetry|mirror symmetry]] as this favours movement.<ref name=":0" />{{Rp|pages=48–49}} Plants often have radial or [[rotational symmetry]], as do many flowers, as well as animals which are largely static as adults, such as [[sea anemone]]s. Fivefold symmetry is found in the [[echinoderms]], including [[starfish]], [[sea urchin]]s, and [[sea lilies]].<ref name=":0" />{{Rp|pages=64–65}}

Among non-living things, [[snowflake]]s 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.<ref name=":0" />{{Rp|page=52}} [[Crystal]]s have a highly specific set of possible [[crystal habit|crystal symmetries]]; they can be cubic or [[octahedral]], but cannot have fivefold symmetry (unlike [[quasicrystals]]).<ref name=":0" />{{Rp|pages=82–84}}

=== Spirals ===

[[File:Aloe polyphylla spiral.jpg|thumb|upright|''[[Aloe polyphylla]]'' [[phyllotaxis]]]]

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]].<ref>{{cite journal | url=http://www.scipress.org/journals/forma/pdf/1904/19040335.pdf | title=Growth in Plants: A Study in Number | author=Kappraff, Jay | journal=Forma | year=2004 | volume=19 | pages=335–354 | access-date=2013-01-18 | archive-date=2016-03-04 | archive-url=https://web.archive.org/web/20160304001606/http://www.scipress.org/journals/forma/pdf/1904/19040335.pdf | url-status=dead }}</ref>
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=== Chaos, turbulence, meanders and complexity ===
[[File:Vortex-street-1.jpg|thumb|upright=0.6|[[Vortex street]] turbulence]]

[[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.<ref>{{cite journal | title=Chaos |author1=Crutchfield, James P |author2=Farmer, J Doyne |author3=Packard, Norman H |author4=Shaw, Robert S | journal=Scientific American |date=December 1986 | volume=254 | issue=12 | pages=46–57|doi=10.1038/scientificamerican1286-46 |bibcode=1986SciAm.255f..46C }}</ref> 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.<ref>{{cite journal |last1=Clerc |first1=Marcel G. |last2=González-Cortés |first2=Gregorio |last3=Odent |first3=Vincent |last4=Wilson |first4=Mario |title=Optical textures: characterizing spatiotemporal chaos |journal=Optics Express |date=29 June 2016 |volume=24 |issue=14 |pages=15478–85 |doi=10.1364/OE.24.015478|pmid=27410822 |arxiv=1601.00844 |bibcode=2016OExpr..2415478C |s2cid=34610459 }}</ref> Many natural patterns are shaped by this complexity, including [[vortex street]]s,<ref>von Kármán, Theodore. ''Aerodynamics''. McGraw-Hill (1963): {{ISBN|978-0070676022}}. Dover (1994): {{ISBN|978-0486434858}}.</ref> other effects of turbulent flow such as [[meander]]s in rivers.<ref>{{cite book | first=Jacques | last=Lewalle | title=Lecture Notes in Incompressible Fluid Dynamics: Phenomenology, Concepts and Analytical Tools | chapter=Flow Separation and Secondary Flow: Section 9.1 | chapter-url=http://www.ecs.syr.edu/faculty/lewalle/FluidDynamics/fluidsCh9.pdf | year=2006 | location=Syracuse, NY | publisher=Syracuse University | url-status=dead | archive-url=https://web.archive.org/web/20110929075022/http://www.ecs.syr.edu/faculty/lewalle/FluidDynamics/fluidsCh9.pdf | archive-date=2011-09-29 }}</ref> or nonlinear interaction of the system <ref>{{cite journal |last1=Scroggie |first1=A.J |last2=Firth |first2=W.J |last3=McDonald |first3=G.S |last4=Tlidi |first4=M |last5=Lefever |first5=R |last6=Lugiato |first6=L.A |title=Pattern formation in a passive Kerr cavity |journal=Chaos, Solitons & Fractals |date=August 1994 |volume=4 |issue=8–9 |pages=1323–1354 |doi=10.1016/0960-0779(94)90084-1|bibcode=1994CSF.....4.1323S |url=https://dipot.ulb.ac.be/dspace/bitstream/2013/127366/1/1994Chaos_Solitons_and_Fractals_4_1323-1354.pdf }}</ref>
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=== Waves, dunes ===
[[File:Sand dune ripples.jpg|thumb|upright|[[Dune]] [[Capillary wave|ripple]]]]
[[File:Mönster - Sand - Brädor - 2021.jpg|thumb|upright|Dune ripples and boards form a symmetrical pattern.]]
[[Wave]]s are disturbances that carry energy as they move. [[Mechanical wave]]s propagate through a medium – air or water, making it [[Oscillation|oscillate]] as they pass by.<ref>French, A.P. ''Vibrations and Waves''. Nelson Thornes, 1971.{{full citation needed|date=February 2024}}</ref> [[Wind wave]]s are [[surface wave]]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]]s.<ref>{{cite conference | first=H.L. | last=Tolman | title=Practical wind wave modeling | book-title=CBMS Conference Proceedings on Water Waves: Theory and Experiment | year=2008 | conference=Howard University, USA, 13–18 May 2008 | publisher=World Scientific Publ. | url=http://polar.ncep.noaa.gov/mmab/papers/tn270/Howard_08.pdf | editor-first=M.F. | editor-last=Mahmood}}</ref>
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=== Bubbles, foam ===

[[File:Foam - big.jpg|thumb|upright|[[Foam]] of [[soap bubble]]s]]

[[Foam]]s 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 [[radiolarian]]s, [[sponge]] [[spicule (sponge)|spicule]]s, and the skeletons of [[silicoflagellate]]s and [[sea urchin]]s.<ref>Ball, Philip. ''Shapes'', 2009. pp. 68, 96-101.{{full citation needed|date=February 2024}}</ref><ref>[[Frederick J. Almgren, Jr.]] and [[Jean E. Taylor]], ''The geometry of soap films and soap bubbles'', Scientific American, vol. 235, pp. 82–93, July 1976.</ref>
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=== Cracks ===
[[File:Cracked earth in the Rann of Kutch.jpg|thumb|upright|Shrinkage [[Fracture|Cracks]]]]

[[Fracture|Crack]]s 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.<ref>Stevens, Peter. 1974. Page 207.</ref>
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=== Spots, stripes===
{{multiple image |direction=horizontal |total_width=440
|image1=Giant Pufferfish skin pattern detail.jpg|caption1=[[Mbu pufferfish]] skin
|image2=Animal skin.jpg|caption2=Skins of a [[South African giraffe]] and [[Burchell's zebra]]
}}
{{main|Pattern formation}}

[[Alan Turing]],<ref name=Turing>{{Cite journal| last= Turing | first= A. M. | title = The Chemical Basis of Morphogenesis | journal=[[Philosophical Transactions of the Royal Society B]] | volume = 237 | pages = 37–72 | year = 1952 | doi=10.1098/rstb.1952.0012| issue= 641|bibcode = 1952RSPTB.237...37T | s2cid= 937133 | doi-access=  }}</ref> and later the mathematical biologist [[James D. Murray]]<ref name="Murray2013">{{cite book |last=Murray |first=James D. |title=Mathematical Biology|url=https://books.google.com/books?id=K3LmCAAAQBAJ&pg=PA436 |date=9 March 2013 |publisher=Springer Science & Business Media |isbn=978-3-662-08539-4 |pages=436–450}}</ref> 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.<ref name=Ball159>Ball, Philip. ''Shapes'', 2009. pp. 159–167.{{full citation needed|date=February 2024}}</ref> These  [[spatiotemporal pattern]]s slowly drift, the animals' appearance changing imperceptibly as Turing predicted.

== Art and architecture ==
{{further|Mathematics and art|Mathematics and architecture}}

=== Tilings ===
[[File:Enderun library Topkapi 42.JPG|thumb|Elaborate ceramic tiles at [[Topkapi Palace]]]]
{{further|Tessellation|Tile}}

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.<ref>{{cite web | url=http://char.txa.cornell.edu/language/element/pattern/pattern.htm | title=Art, Design, and Visual Thinking | publisher=Cornell University | work=Pattern | year=1995 | access-date=12 December 2012 | author=Jirousek, Charlotte}}</ref> 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.<ref name=Grunbaum>{{cite book|last=Grünbaum|first=Branko|title=Tilings and Patterns|url=https://archive.org/details/isbn_0716711931|url-access=registration|year=1987|publisher=W. H. Freeman|location=New York|author2=Shephard, G. C.|isbn=9780716711933}}</ref>

===In architecture===
[[Image:Hampi1.jpg|thumb|upright|Patterns in architecture: the Virupaksha temple at Hampi has a [[fractal]]-like structure where the parts resemble the whole.]]
{{main|Pattern (architecture)|Mathematics and 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 [[column]]s, [[pediment]]s, and [[lintel]]s.<ref>{{cite book | title=A History of Western Art | publisher=McGraw Hill | author=Adams, Laurie | year=2001 | page=99}}</ref> 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.<ref>{{cite book | title=Heaven's Fractal Net: Retrieving Lost Visions in the Humanities | publisher=Indiana University Press | author=Jackson, William Joseph | year=2004 | page=2}}</ref>
[[File:Evening columns Zeus temple Athens.jpg|thumb|Patterns in Architecture: the columns of Zeus's temple in Athens]]
{{See also|pattern book}}

== Language and linguistics ==
Language provides researchers in [[linguistics]] with a wealth of patterns to investigate,<ref>
{{cite book
 |last1                = Busse
 |first1               = Beatrix
 |author-link1         = Beatrix Busse
 |last2                = Moehlig-Falke
 |first2               = Ruth
 |editor-last1         = Busse
 |editor-first1        = Beatrix
 |editor-link1         = Beatrix Busse
 |editor-last2         = Moehlig-Falke
 |editor-first2        = Ruth
 |date                 = 16 December 2019
 |chapter              = Patterns in linguistics
 |title                = Patterns in Language and Linguistics: New Perspectives on a Ubiquitous Concept
 |url                  = https://books.google.com/books?id=80jSDwAAQBAJ
 |series               = Topics in English Linguistics [TiEL], volume 104
 |publication-place    = Berlin
 |publisher            = Walter de Gruyter GmbH & Co KG
 |page                 = 1
 |isbn                 = 9783110596656
 |access-date          = 13 April 2025
 |quote                = [...] the concept of ''pattern'' [...] used in different fields of linguistics, including corpus linguistics, sociolinguistics, historical/diachronic linguistics, construction grammar, discourse linguistics, psycholinguistics, language acquisition, phonology and second-language learning.
}}
</ref>
and [[literary studies]] can investigate patterns in areas such as sound, grammar,  motifs, metaphor, imagery, and narrative plot.<ref>
{{cite book
 |last1                = Thornborrow
 |first1               = Joanna
 |last2                = Wareing
 |first2               = Shân
 |year                 = 1998
 |title                = Patterns in Language: An Introduction to Language and Literary Style
 |url                  = https://books.google.com/books?id=fmWMnbVMxoMC
 |series               = Interface Series, ISSN 0955-730X
 |publication-place    = London
 |publisher            = Psychology Press
 |isbn                 = 9780415140645
 |access-date          = 13 April 2025
}}
</ref>

== Science and mathematics ==
[[File:Fractal fern explained.png|thumb|upright|Fractal model of a fern illustrating [[self-similar]]ity]]

[[Mathematics]] is sometimes called the "Science of Pattern", in the sense of rules that can be applied wherever needed.<ref>{{cite journal | title=Mathematics as a Science of Patterns: Ontology and Reference | author=Resnik, Michael D. | journal=Noûs |date=November 1981 | volume=15 | issue=4 | pages=529–550 | doi=10.2307/2214851| jstor=2214851 }}</ref> 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.<ref>{{cite web | url=http://www.coas.howard.edu/mathematics/faculty/bayne/patterns.html | title=MATH 012 Patterns in Mathematics - spring 2012 | year=2012 | access-date=16 January 2013 | author=Bayne, Richard E | archive-date=7 February 2013 | archive-url=https://web.archive.org/web/20130207065047/http://www.coas.howard.edu/mathematics/faculty/bayne/patterns.html | url-status=dead }}</ref>

[[Gravity]] is a source of ubiquitous scientific patterns or patterns of observation. The rising and falling pattern of the sun each day results from the rotation of the earth while in orbit around the sun. Likewise, the [[moon|moon's]] path through the sky is due to its orbit of the earth. These examples, while perhaps trivial, are examples of the "unreasonable effectiveness of mathematics" which obtain due to the [[differential equations]] whose application within [[physics]] function to describe the most general [[empirical]] patterns of the [[universe]].<ref>{{cite journal |last1 =Steen |first1 =Lynn |date =June 1988 |title =The Science of Patterns |url =https://www.science.org/doi/pdf/10.1126/science.240.4852.611 |journal =Science |volume =240 |issue =4852 |pages =611–616 |doi =10.1126/science.240.4852.611 |pmid =17840903 |bibcode =1988Sci...240..611S |access-date =2024-08-11|url-access =subscription }} The author attributes Eugene Wigner for the claim for the "unreasonable effectiveness of mathematics," a partial quote which continues "[t]he miracle of the appropriateness of the language of
mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve."</ref>

=== Real patterns<!--'Real patterns' redirects here--> ===
[[Daniel Dennett]]'s notion of '''real patterns'''<!--boldface per WP:R#PLA-->, discussed in his 1991 paper of the same name,<ref>Dennett, D. C. (1991). Real Patterns. ''The Journal of Philosophy'' '''88'''(1), 27–51.</ref> provides an ontological framework aiming to discern the reality of patterns beyond mere human interpretation, by examining their predictive utility and the efficiency they provide in compressing information. For example, [[Center of mass|centre of gravity]] is a real pattern because it allows the prediction of the movements of a bodies such as the earth around the sun, and it compresses all the information about all the particles in the sun and the earth that allows scientists to make those predictions.

=== 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. [[Fractal]]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 coastlines and tree-shapes, which repeat their shape regardless of the magnification used by the viewer. 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 system]]s describing [[tree]]-shapes).<ref name="Mandelbrot1983">{{cite book |last =Mandelbrot |first =Benoit B. |author-link =Benoit Mandelbrot |title =The fractal geometry of nature
|url =https://books.google.com/books?id=0R2LkE3N7-oC |year =1983| publisher =Macmillan
|isbn =978-0-7167-1186-5}}</ref>

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.<ref>{{cite book | title =Pattern Theory: From Representation to Inference | publisher =Oxford University Press |author1 =Grenander, Ulf |author2 =Miller, Michael | year =2007}}</ref>

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.<ref>{{cite web | url =http://www.cfa.harvard.edu/smg/Website/UCP/ | title =Causal Patterns in Science | publisher =Harvard Graduate School of Education | year =2008 | access-date =16 January 2013}}</ref>

A 2021 study, "Aesthetics and Psychological Effects of Fractal Based Design",<ref>{{Cite journal |last1 =Robles |first1 =Kelly E. |last2 =Roberts |first2 =Michelle |last3 =Viengkham |first3 =Catherine |last4 =Smith |first4 =Julian H. |last5 =Rowland |first5 =Conor |last6 =Moslehi |first6 =Saba |last7 =Stadlober |first7 =Sabrina |last8 =Lesjak |first8 =Anastasija |last9 =Lesjak |first9 =Martin |last10 =Taylor |first10 =Richard P. |last11 =Spehar |first11 =Branka |last12 =Sereno |first12 =Margaret E. |date =2021 |title =Aesthetics and Psychological Effects of Fractal Based Design |journal =Frontiers in Psychology |volume =12 |doi =10.3389/fpsyg.2021.699962 |pmid =34484047 |pmc =8416160 |issn =1664-1078 |doi-access =free }}</ref> suggested that 

<blockquote>
fractal patterns possess self-similar components that repeat at varying size scales. The perceptual experience of human-made environments can be impacted with inclusion of these natural patterns. Previous work has demonstrated consistent trends in preference for and complexity estimates of fractal patterns. However, limited information has been gathered on the impact of other visual judgments. Here we examine the aesthetic and perceptual experience of fractal 'global-forest' designs already installed in humanmade spaces and demonstrate how fractal pattern components are associated with positive psychological experiences that can be utilized to promote occupant wellbeing. These designs are composite fractal patterns consisting of individual fractal 'tree-seeds' which combine to create a 'global fractal forest.' The local 'tree-seed' patterns, global configuration of tree-seed locations, and overall resulting 'global-forest' patterns have fractal qualities. These designs span multiple mediums yet are all intended to lower occupant stress without detracting from the function and overall design of the space. In this series of studies, we first establish divergent relationships between various visual attributes, with pattern complexity, preference, and engagement ratings increasing with fractal complexity compared to ratings of refreshment and relaxation which stay the same or decrease with complexity. Subsequently, we determine that the local constituent fractal ('tree-seed') patterns contribute to the perception of the overall fractal design, and address how to balance aesthetic and psychological effects (such as individual experiences of perceived engagement and relaxation) in fractal design installations. This set of studies demonstrates that fractal preference is driven by a balance between increased arousal (desire for engagement and complexity) and decreased tension (desire for relaxation or refreshment). Installations of these composite mid-high complexity 'global-forest' patterns consisting of 'tree-seed' components balance these contrasting needs, and can serve as a practical implementation of biophilic patterns in human-made environments to promote occupant wellbeing.
</blockquote>

== See also ==
{{div col|colwidth=20em}}
* [[Archetype]]
* [[Cellular automata]]
* [[Die (manufacturing)]] (template)
* [[Form constant]]
* [[Fractal]]
* [[Pattern (architecture)]]
* [[Pattern (casting)]]
* [[Pattern coin]]
* [[Pattern matching]]
* [[Pattern (sewing)]]
* [[Pattern recognition]]
* [[Patterns in nature]]
* [[Pedagogical patterns]]
* [[Software design pattern]]
* [[Template method pattern]]
{{div col end}}
<!--Please don't add anything here, all these items should be incorporated in text and referenced-->
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==Notes==

{{notelist}}
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== References ==

{{reflist|30em}}

== Bibliography ==
{{Wiktionary|pattern}}
{{Commons category|Patterns}}
{{Wikiquote}}

=== 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.]] ''[https://archive.org/details/ongrowthform00thom  On Growth and Form]''. 1942 2nd ed. (1st ed., 1917). {{ISBN|0-486-67135-6}}

=== In art and architecture === <!-- Not Computing! for that, see below -->

* [[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 ===

<!-- Alexander, C. is listed under Art and Architecture above -->
* Gamma, E., Helm, R., Johnson, R., Vlissides, J. ''[[Design Patterns]]''. Addison-Wesley, 1994.
* Bishop, C. M. ''Pattern Recognition and Machine Learning''. Springer, 2007.

<!--please don't add links to your patterns site here, they will be deleted-->
{{metaphysics}}

[[Category:Patterns| ]]
[[Category:Concepts in epistemology]]
[[Category:Metaphysical properties]]
[[Category:Concepts in the philosophy of mind]]
[[Category:Concepts in the philosophy of science]]
[[Category:Design]]
Hazem's Pattern
[[File:Drawing of Hazem's phone pattern.svg|thumb]]