- References could be improved
These elements repeat in a predictable manner. It can be a template or model which can be used to generate things or parts of a thing, especially if the things that are created 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. A single template, tile, or cell, is combined with duplicates without change or modification. For example, simple harmonic oscillators produce repeated patterns of movement.
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, even generate a pattern using an affine transformation which combines translation, scaling, rotation and reflection.
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
Two factor authentication
In two factor authentication, user has to remember his own "Pattern" instead of traditional password. This pattern is some sequence of positions, for example it is sequence of cells from of an Array-Card. This pattern acts as one of the factor, which user know.
Any of the five senses may directly observe patterns.
One recurring pattern in a single piece of art may constitute a motif.
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. This is still used by many artists).
- "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.
Patterns of abstraction may not be directly observable - such as patterns in science, drama, maths, english
Mathematics is commonly described as the "Science of Pattern." Any sequence of numbers that may be modeled by a mathematical function is 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.
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.
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 extremely simple (e.g. Lindenmayer systems for the description of tree shapes).
In computer science, complex mathematical models may be designed to create more complex patterns. Patterns may be found in every branch of computer science.
An important use of patterns in computer science is the idea of Design patterns. Design patterns are general solutions to problems in object-oriented programming. They will not solve a specific problem, but they provide a sort of architectural outline that may be reused in order to speed up the development process of a program. Design patterns have provided the stepping stone for computer science to truly enter the engineering field.
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.
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.
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.
- Pattern formation
- Pattern (sewing)
- Pattern coin
- Pattern (casting)
- Pattern language
- Pedagogical patterns
- Pattern (architecture)
- Design pattern
- Pattern recognition
- Design pattern (computer science)
- Honarkhah, M and Caers, J, 2010, Stochastic Simulation of Patterns Using Distance-Based Pattern Modeling, Mathematical Geosciences, 42: 487 - 517
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- Mathematics as a Science of Patterns at Convergence
- Geometric Arts
- Wiki patterns and anti-patterns
- Fluctuation patterns in high-frequency financial asset returns
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