Tilings, such as these from Igreja de Campanha Azulejo in Portugal, are examples of visual patterns used for decoration

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A pattern, from the French patron, is a type of theme of recurring events or objects, sometimes referred to as elements of a set of objects.

The elements of a pattern repeat in a predictable manner. Patterns can be based on a template or model which generates pattern elements, especially if the elements have enough in common for the underlying pattern to be inferred, in which case the things are said to exhibit the unique pattern.

The most basic patterns, called Tessellations, are based on repetition and periodicity. In tessellation, a single template, tile, or cell is repeated without change or modification, usually in two dimensions to form a flat patterned surface.

Other patterns, such as Penrose tiling and Pongal or Kolam patterns from India, use symmetry which is a form of finite repetition, instead of translation which can repeat to infinity. Fractal patterns also use magnification or scaling giving an effect known as self-similarity or scale invariance. Some plants, like Ferns, generate a pattern using an affine transformation which combines translation, scaling, rotation and reflection.

A different kind of pattern generator is a simple harmonic oscillator, which produces repeated movements in time.

Pattern matching is the act of checking for the presence of the constituents of a pattern, whereas the detecting for underlying patterns is referred to as pattern recognition. The question of how a pattern emerges is accomplished through the work of the scientific field of pattern formation.

Pattern recognition is more complex when templates are used to generate variants. For example, in English, sentences often follow the "N-VP" (noun - verb phrase) pattern, but some knowledge of the English language is required to detect the pattern. Computer science, ethology, and psychology are fields which study patterns.

"A pattern has an integrity independent of the medium by virtue of which you have received the information that it exists. Each of the chemical elements is a pattern integrity. Each individual is a pattern integrity. The pattern integrity of the human individual is evolutionary and not static."

R. Buckminster Fuller (1895-1983), U.S.American philosopher and inventor, in Synergetics: Explorations in the Geometry of Thinking (1975), Pattern Integrity 505.201

Observable patterns [link]

Any of the five senses may directly observe patterns. Conversely, abstract patterns as in in science, maths, or language may be observable only by analysis.

Visual [link]

Common visual patterns include simple decorations such as stripes, zigzags, and polka dots, but may be arbitrarily complex. Visual patterns are widespread in nature and in art.

• Penrose tilings

Nature [link]

A honeycomb is a tiling of hexagonal cells, while worker bees form a random pattern of nearly-repeating elements on top of it

Nature provides examples of many kinds of pattern, including tessellations and fractals.

Many natural patterns are chaotic, never exactly repeating though consisting of many similar elements.^{[citation needed]}

The golden ratio (approximately 1.618) is found frequently in nature. It is defined by two numbers, that form a ratio such that (a+b)/a = a/b (a/b being the golden ratio). This pattern was exploited by Leonardo da Vinci in his art. The golden ratio can be seen in nature, from the spirals of flowers to the symmetry of the human body (as expressed in Da Vinci's Vitruvian Man, one of the most referenced and reproduced works of art today. The golden ratio is still used by artists.^{[citation needed]}

Art [link]

A recurring pattern in a single piece of art may constitute a motif.^{[citation needed]}

"Art is the imposing of a pattern on experience, and our aesthetic enjoyment is recognition of the pattern."

Alfred North Whitehead (1861-1947), English philosopher and mathematician. Dialogues, June 10, 1943.

Mathematics [link]

Mathematics is sometimes called the "Science of Pattern." Any sequence of numbers that may be modeled by a mathematical function can be considered a pattern.

In Pattern theory, mathematicians attempt to describe the world in terms of patterns. The goal is to lay out the world in a more computationally friendly manner.^{[citation needed]}

Patterns are common in many areas of mathematics. Recurring decimals are one example. These are repeating sequences of digits which repeat infinitely. For example, 1 divided by 81 will result in the answer 0.012345679... the numbers 0-9 (except 8) will repeat forever — 1/81 is a recurring decimal.^{[citation needed]}

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 the outer appearance of self-similar patterns can be quite complex, the rules needed to describe or produce their formation can be simple (e.g. Lindenmayer systems describing tree shapes).^{[citation needed]}

Spatial Statistics [link]

In multiple-point Geostatistics, a training image is used to provide the spatial model of variability. A pattern-based modeling approach can thus be seen as an image construction algorithm, where the patterns of the training image are used, and tiled next to each other such that a new image with similar characteristics/features is generated.^[1]

Computer science [link]

Patterns may be found in every branch of computer science.

Design patterns [link]

An important use of patterns in computer science is the idea of Design patterns. Design patterns are general solutions to problems in programming. They do not offer solutions to specific problems, but provide a reusable architectural outline that may speed the development of computer programs.^{[citation needed]}

Image compression [link]

Low quality (46:1) 0.41 b/pxl

Lowest quality (144:1) 0.13 b/pxl

Excessive JPEG image compression
Click on each image to see the fine patterns clearly

A completely different use of patterns is the JPEG compressed image format. The image is divided into a grid pattern of equal-size tiles. Then each tile is analysed independently to find the dominant patterns in the part of the image it contains. As more compression is applied, the best-match tiles are chosen from a smaller set of available tiles. If excessive compression is applied then both the tiles and the patterns within tiles may be seen.^{[citation needed]}

Science [link]

In geology, a mineral's crystal structure expresses a recurring pattern. In fact, this is one of the five requirements of a mineral. Minerals must have a fixed chemical composition in a repeating arrangement, such as a crystal matrix. A 2-dimensional crystal structure has 10 different possible planar lattices. Moving up to 3 dimensions, 32 patterns are possible. These are called bravais lattices.^{[citation needed]}

Language [link]

This section requires expansion.

See also [link]

• Pattern formation
• Pattern (sewing)
• Pattern coin
• Pattern (casting)
• Pedagogical patterns
• Pattern (architecture)
• Pattern recognition
• Cellular Automata

Bibliography [link]

Patterns in art and architecture [link]

• 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 nature [link]

• Ball, P. The Self-made Tapestry: Pattern Formation in Nature. Oxford, 2001.
• Edmaier, B. Patterns of the Earth. Phaidon, 2007.
• Haeckel, E. Art Forms in Nature. Dover, 1974.
• Stevens, P.S. Patterns in Nature. Penguin, 1974.

Patterns in science and mathematics [link]

• 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 [link]

• Gamma, E., Helm, R., Johnson, R., Vlissides, J. Design Patterns. Addison-Wesley, 1994.
• Bishop, C.M. Pattern Recognition and Machine Learning. Springer, 2007.

References [link]

External links [link]

Look up pattern in Wiktionary, the free dictionary.

• Mathematics as a Science of Patterns at Convergence
• Geometric Arts
• Patternity