digplanet beta 1: Athena
Share digplanet:

Agriculture

Applied sciences

Arts

Belief

Chronology

Culture

Education

Environment

Geography

Health

History

Humanities

Language

Law

Life

Mathematics

Nature

People

Politics

Science

Society

Technology

For other uses, see Pattern (disambiguation).
Tilings, such as these from Igreja de Campanhã, Porto, Portugal, are visual patterns used for decoration.

A pattern, apart from the term's use to mean "Template"[a], is a discernible regularity in the world or in a manmade design. As such, the elements of a pattern repeat in a predictable manner. A geometric pattern is a kind of pattern formed of geometric shapes and typically repeating like a wallpaper.

Any of the five 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 are often chaotic, never exactly repeating, and often involve fractals. Natural patterns include spirals, meanders, waves, foams, tilings, cracks, and those created by symmetries of rotation and reflection. Patterns have an underlying mathematical structure;[1] 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 is a known solution to a class of problems in programming. In fashion, the pattern is a template used to create any number of similar garments.

## Nature

Main article: Patterns in nature

Nature provides examples of many kinds of pattern, including symmetries, trees and other structures with a fractal dimension, spirals, meanders, waves, foams, tilings, cracks and stripes.[2]

### Symmetry

Symmetry is widespread in living things. Animals that move usually have bilateral or mirror symmetry as this favours movement.[3] Plants often have radial or rotational symmetry, as do many flowers, as well as animals which are largely static as adults, such as sea anemones. Fivefold symmetry is found in the echinoderms, including starfish, sea urchins, and sea lilies.[4]

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.[5] Crystals have a highly specific set of possible crystal symmetries; they can be cubic or octahedral, but cannot have fivefold symmetry (unlike quasicrystals).[6]

### Spirals

Spiral patterns are found in the body plans of animals including molluscs such as the nautilus, and in the phyllotaxis of many plants, both of leaves spiralling around stems, and in the multiple spirals found in flowerheads such as the sunflower and fruit structures like the pineapple.[7]

### Chaos, flow, meanders

Vortex street turbulence

Chaos theory predicts that while the laws of physics are deterministic, events and patterns in nature never exactly repeat because extremely small differences in starting conditions can lead to widely differing outcomes.[8] Many natural patterns are shaped by this apparent randomness, including vortex streets[9] and other effects of turbulent flow such as meanders in rivers.[10]

### Waves, dunes

Waves are disturbances that carry energy as they move. Mechanical waves propagate through a medium – air or water, making it oscillate as they pass by.[11] 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.[12]

### Bubbles, foam

Foams obey Plateau's 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 radiolarians, sponge spicules, and the skeletons of silicoflagellates and sea urchins.[13][14]

### Cracks

Shrinkage 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.[15]

### Spots, stripes

Main article: Pattern formation

Alan Turing,[16] and later the mathematical biologist James Murray, 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.[17] These patterns slowly drift, the animals' appearance changing imperceptibly as Turing predicted.

## Art and architecture

Elaborate ceramic tiles at Topkapi Palace

### Tilings

Further information: Tessellation and 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 tiling or carpet, but a pattern need not necessarily repeat exactly as long as it provides some form or organizing "skeleton" in the artwork.[18] 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.[19]

### In architecture

Patterns in architecture: the Virupaksha temple at Hampi has a fractal-like structure where the parts resemble the whole.

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 columns, pediments, and lintels.[20] 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.[21]

## Science and mathematics

Fractal model of a fern illustrating self-similarity

Mathematics is sometimes called the "Science of Pattern", in the sense of rules that can be applied wherever needed.[22] 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.[23]

### Fractals

Some mathematical rule-patterns can be visualised, and among these are those that explain patterns in nature including the mathematics of symmetry, waves, meanders, and fractals. Fractals are mathematical patterns that are scale invariant. This means that the shape of the pattern does not depend on how closely you look at it. Self-similarity is found in fractals. Examples of natural fractals are coast lines and tree shapes, which repeat their shape regardless of what magnification you view at. While self-similar patterns can appear indefinitely complex, the rules needed to describe or produce their formation can be simple (e.g. Lindenmayer systems describing tree shapes).[24]

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.[25]

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.[26]

## Computer science

In computer science, a software design pattern, in the sense of a template, is a general solution to a problem in programming. A design pattern provides a reusable architectural outline that may speed the development of many computer programs.[27]

## Fashion

Main article: Pattern (sewing)

In fashion, the pattern is a template, a technical two-dimensional tool used to create any number of identical garments. It can be considered as a means of translating from the drawing to the real garment.[28]

## Bibliography

### Patterns 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.

### Patterns 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.

### Patterns 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.

## Notes

1. ^ From the French patron ('template')

## References

1. ^ Stewart, 2001. Page 6.
2. ^ Stevens, Peter. Patterns in Nature, 1974. Page 3.
3. ^ Stewart, Ian. 2001. Pages 48-49.
4. ^ Stewart, Ian. 2001. Pages 64-65.
5. ^ Stewart, Ian. 2001. Page 52.
6. ^ Stewart, Ian. 2001. Pages 82-84.
7. ^ Kappraff, Jay (2004). "Growth in Plants: A Study in Number". Forma 19: 335–354.
8. ^ Crutchfield, James P; Farmer, J Doyne,; Packard, Norman H; Shaw, Robert S (December 1986). "Chaos". Scientific American 254 (12): 46–57.
9. ^ von Kármán, Theodore. Aerodynamics. McGraw-Hill (1963): ISBN 978-0070676022. Dover (1994): ISBN 978-0486434858.
10. ^ Lewalle, Jacques (2006). "Flow Separation and Secondary Flow: Section 9.1". Lecture Notes in Incompressible Fluid Dynamics: Phenomenology, Concepts and Analytical Tools. Syracuse, NY: Syracuse University..
11. ^ French, A.P. Vibrations and Waves. Nelson Thornes, 1971.
12. ^ Tolman, H.L. (2008), "Practical wind wave modeling", in Mahmood, M.F., CBMS Conference Proceedings on Water Waves: Theory and Experiment, Howard University, USA, 13–18 May 2008: World Scientific Publ.
13. ^ Philip Ball. Shapes, 2009. pp 68, 96-101.
14. ^ 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.
15. ^ Stevens, Peter. 1974. Page 207.
16. ^ Turing, A. M. (1952). "The Chemical Basis of Morphogenesis". Philosophical Transactions of the Royal Society B 237 (641): 37–72. Bibcode:1952RSPTB.237...37T. doi:10.1098/rstb.1952.0012.
17. ^ Ball, Philip. Shapes. 2009. Pages 159–167.
18. ^ Jirousek, Charlotte (1995). "Art, Design, and Visual Thinking". Pattern. Cornell University. Retrieved 12 December 2012.
19. ^ Grünbaum, Branko; Shephard, G. C. (1987). Tilings and Patterns. New York: W. H. Freeman.
20. ^ Adams, Laurie (2001). A History of Western Art. McGraw Hill. p. 99.
21. ^ Jackson, William Joseph (2004). Heaven's Fractal Net: Retrieving Lost Visions in the Humanities. Indiana University Press. p. 2.
22. ^ Resnik, Michael D. (November 1981). "Mathematics as a Science of Patterns: Ontology and Reference". Noûs 15 (4): 529–550. doi:10.2307/2214851.
23. ^ Bayne, Richard E (2012). "MATH 012 Patterns in Mathematics - spring 2012". Retrieved 16 January 2013.
24. ^ Mandelbrot, Benoît B. (1983). The fractal geometry of nature. Macmillan. ISBN 978-0-7167-1186-5.
25. ^ Grenander, Ulf; Miller, Michael (2007). Pattern Theory: From Representation to Inference. Oxford University Press.
26. ^ "Causal Patterns in Science". Harvard Graduate School of Education. 2008. Retrieved 16 January 2013.
27. ^ Gamma et al, 1994.
28. ^ Loppa, 2003.
 1000000 videos foundNext >
 How to draw a Paisley PatternThis is a very old pattern that comes originally from the middle and far east. It's thought originally to have been based on the shape of a palm from or mayb... Zendoodle Sampler Zentangle Pattern Styles Tutorial 2http://www.milliande.com/Zendoodle-Sampler-Zentangle-Pattern-Styles-Tutorial.html Zendoodle Pattern sheet Fills free to download SHARE YOUR favourite Zendo... Learning AB Patterns / What's Next? / Part 1Learning Patterns is fun. Start with the AB Pattern. Can you figure out what's next? See the AB Pattern in action. Children in preschool and kindergarten wil... How to Create Patterns from Existing Clothing - Simple TopsUse your existing simple tops to create new patterns so that you can make more of all your favorite shirts. Check out other great fashion related videos on t... How to Draft a Simple Skirt Pattern, CRAFTOVISIONThis the first video in my custom skirt course where I teach you how to draft a simple skirt pattern from your measurements. Want to be on an episode? Email ... Illustrator CS6: Using the Pattern Options tool | lynda.com tutorialThis Illustrator CS6 tutorial discusses how to create repeatable patterns in different styles and configurations using the new Pattern Options tool. Watch mo... Doodle - Circular Pattern DesignFirst time watching my video? ❖ Visit my channel : Pic Candle http://bit.ly/PicCandle ❖ Subscribe for more Doodles : http://bit.ly/PicCandleSubscribe .......... How to Cut Out Sewing Pattern PiecesIn order to sew more complicated projects, its important to know how to cut out a commercial pattern. When pulling out the pattern pieces, it can be very ove... #Crochet Baby Blanket Pattern (subtitulos en Espanol)In this video you will learn how to #crochet this pattern that is ideal for a #baby blanket, scarf, etc. You simply repeat the pattern for your desired size.... Surgeon - Fixed Action PatternSurgeon will debut on Token with a two-track EP called Fixed Action Pattern. Due out on August 25th, the record serves as a precursor to Aphelion, a compilat...
 1000000 videos foundNext >
 1035193 news items
 Route 22 traffic pattern in Easton changes tonight in Easton-Phillipsburg ... The Express-Times - lehighvalleylive.com Tue, 02 Sep 2014 07:48:45 -0700 The Easton-Phillipsburg toll bridge rehabilitation protect turns into the "homestretch" this week with the traffic pattern moving to the far right lanes in either direction on Route 22. Currently, traffic is moving in single lanes on the eastbound side ... Boing Boing Is moth wing pattern a sign from God or Satan? Boing Boing Mon, 01 Sep 2014 09:07:30 -0700 puzzling-moth When Yvonne Esquilin of Georgetown, Texas found a moth in her house, she interpreted its wing pattern as a sign from God. "At first it looked like Jesus and I still think it looks like Jesus," she told KXAN news. After her family shared ... WDBJ7 New traffic pattern along Elm Avenue in Roanoke starts Wednesday WDBJ7 Tue, 02 Sep 2014 12:18:45 -0700 Drivers traveling east will be moved to the newly constructed portion of the bridge, while those heading west will remain on the current traffic pattern in place. On Tuesday and Wednesday, the left lane will be closed to traffic heading both east and ... Stray rescue noticing a pattern of abuse KSDK Mon, 01 Sep 2014 19:48:45 -0700 Stray rescue noticing a pattern of abuse. Some animal activists in St. Louis say they're seeing some especially cruel cases of animal abuse. Loading… Post to Facebook. Stray rescue noticing a pattern of abuse Some animal activists in St. Louis say ... The Guardian The 'Clive Palmer pattern' repeats, and it's proving costlier than ever The Guardian Tue, 02 Sep 2014 00:52:30 -0700 At the end of the last chaotic session of parliament I wrote that a “Palmer pattern” was emerging – cause maximum disruption and then support the government after extracting cobbled-together concessions during chaotic backroom meetings from which all ... Longmont United adopts new vein pattern recognition system Longmont Times-Call Mon, 01 Sep 2014 11:33:45 -0700 Longmont United Hospital is the first hospital in Colorado to use the PatientSecure Biometric ID system to register patients. A reader scans a person's vein pattern in their palm and an algorithm converts that scan to a numeric formula that is ... FxPips.com Bearish GBP/USD Pattern in Focus- USD/CAD to Target 1.1000? DailyFX Tue, 02 Sep 2014 08:22:30 -0700 Remains at risk of a further decline as the descending channel remains in play, while the Relative Strength Index (RSI) dips back into oversold territory; next key objective is the March low (1.6458). Need to see a larger dissent within the Bank of ... Chinese jet's run-in with P-8 seen as pattern Military Times Tue, 02 Sep 2014 09:57:16 -0700 A P-8 maritime surveillance aircraft flies in its first international air show on Nov. 18 at Dubai 2013. A spate of low-level military confrontations between China and the U.S., the most recent on Aug. 19 involving a Navy P-8 Poseidon that was flying a ...
 Limit to books that you can completely read online Include partial books (book previews) .gsc-branding { display:block; }

Oops, we seem to be having trouble contacting Twitter