For more meanings of Pattern, see Pattern (disambiguation)

The pattern is a form, template, or model (or, more abstractly, a set of rules) which can be used to make or 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 pattern. Pattern matching is the act of checking for the presence of the constituents of a pattern. The detection of underlying patterns is called pattern recognition. The question of how different patterns emerge is accomplished through the work of the scientific field of pattern formation. Patterns are also related to repeated shapes or objects, sometimes referred to as elements of the series. Some patterns (for example, many visual patterns) may be directly observable through the senses.

Some patterns are named. Simple decorative examples are stripes , zigzags, and polka-dots. Further examples include the regular tiling of a plane, echoes, and balanced binary branching.

The simplest patterns are based on repetition/periodicity: several copies of a single template are combined without modification. For example, in aviation, a "holding pattern" is a flight path which can be repeated until the aircraft has been granted clearance for landing.

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. Pattern recognition is studied in many fields, including psychology, ethology, and Computer Science.

In addition to static patterns, Simple Harmonic Oscillators produce repeated patterns of movement.

Computer Science

Theory of Computation attempts to grasp the patterns that appear within the logic of computer science. Since efficiency is extremely important when executing a command some million times per second, minimizing a pattern into its most basic form becomes evermore necesssary.

• Pattern matching
• Design patterns
• Regular expressions

Golden Ratio

A recurring theme found in the biology of nature is the golden ratio, approximately 1.6180339887. Two numbers a and b keep the golden ratio when (a+b)/a = a/b, in this case a/b equals the golden ratio. It has a direct relationship to the Fibonacci numbers. This pattern was exploited by Leonardo da Vinci in his art. The Fibonacci pattern has a closed-form expression. These patterns 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.

Art

• Modern art: Mondrian, Op Art
• Impressionism: Pointillism
• Performance Art: Crop circles
• Music: Minimalism

Science and mathematics

Fractals are mathematical patterns. Naturally occurring patterns obey certain principles also found in fractals, for example self-similarity. Even though self-similarity in nature is only approximate and stochastic, integral measures describing fractal properties can also be applied to natural "fractals" like coastal lines, tree shapes, etc. (see fractal geometry). 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).

Patterns are also common in other areas of mathematics. Recurring decimals will repeat a sequence of digits an infinite number of times. 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.

A BuckyBall is named after the chemist who predicted it, Buckminster Fuller. It's a sphere of repeating carbon atoms, linking together to create the surface area of a sphere. Carbon atoms are linked in a repeating 3-carbon bond with one another.

A recurring pattern is one of the 5 cornerstones of the definition of a mineral in geology. A mineral must show it's elements in a three-dimensional recurring pattern (aka a crystal matrix). In two dimensional geology, there are ten different planar lattices possible. In three dimensional geology, there are 32 possible patterns available, called bravais lattices.

• Crystals
• Tessellation
• Penrose tilings
• Cellular Automata
• Mineral

Geometry

The recurring pattern of regular polygons is called a tessellation. There are only three regular polygons that can create a repeating pattern; the square, triangle, and hexagon. Of these, the hexagon is the most stable one in terms of engineering, as any shear stress upon tiles of such is distributed throughout the six points.

Patterns in Pedagogics

• Pedagogical patterns

Quotation

"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. Critical Path, 1981.

"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 is commonly described as the "Science of Pattern."

See also

• Pattern recognition
• DNA motifs
• Pattern (sewing)
• Form constant
• A Pattern Language
• Fibonacci Number

External links

• Mathematics as a Science of Patterns at Convergence
• Geometric Arts
• Wiki patterns and anti-patterns
• Pumpkin Carving Patterns