A pattern, from the French French is a Romance language spoken, around the world, by more than 100 million people as a first language (mother tongue), by 190 million as a second language, and by about another 200 million people as an acquired foreign language, with significant speakers in 54 countries. Most native speakers of the language live in France, where the language patron, is a type of theme of recurring events of or objects, sometimes referred to as elements of a set A set is a collection of distinct objects, considered as an object in its own right. Sets are one of the most fundamental concepts in mathematics. Although it was invented at the end of the 19th century, set theory is now a ubiquitous part of mathematics, and can be used as a foundation from which nearly all of mathematics can be derived. In. 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. Pattern matching In computer science, pattern matching is the act of checking for the presence of the constituents of a given pattern. In contrast to pattern recognition, the pattern is rigidly specified. Such a pattern concerns conventionally either sequences or tree structures. Pattern matching is used to test whether things have a desired structure, to find 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 Pattern recognition is "the act of taking in raw data and taking an action based on the category of the data".[citation needed] Most research in pattern recognition is about methods for supervised learning and unsupervised learning. The question of how a pattern emerges is accomplished through the work of the scientific field of pattern formation The science of pattern formation deals with the visible, orderly outcomes of self-organisation and the common principles behind similar patterns.

The most basic patterns are based on repetition and periodicity. A single template, or cell, is combined with duplicates without change or modification. For example, simple harmonic oscillators produce repeated patterns of movement.

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 English is a West Germanic language that originated in Anglo-Saxon England. As a result of the military, economic, scientific, political, and cultural influence of the British Empire during the 18th, 19th, and early 20th centuries and of the United States since the mid 20th century, it has become the lingua franca in many parts of the world. It is 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 Richard Buckminster “Bucky” Fuller was an American architect, author, designer, futurist, inventor, and visionary (1895-1983), U.S.American philosopher and inventor, in Synergetics: Explorations in the Geometry of Thinking (1975), Pattern Integrity 505.201

Observable Patterns

Patterns may be directly observed with any of our five senses.

Visual

Visual patterns are very common such as simple decorative patterns (stripes, zigzags, and polka-dots). Others can be more complicated, however, they may be found anywhere in nature and in art.

• Penrose tilings

Art

A recurring pattern in a piece of art is referred to as a motif In art, a motif (help·info) is a repeated idea, pattern, image, or theme. Paisley designs are referred to as motifs. Many designs in mosques in Islamic culture are motifs, especially those of flowers. Two major Roman motifs are egg and tongue, and ball and reel.

The golden ratio In mathematics and the arts, two quantities are in golden ratio if the ratio of the sum of the quantities to the larger one equals the ratio of the larger one to the smaller. The golden ratio is an irrational mathematical constant, approximately 1.6180339887. Other names frequently used for the golden ratio are golden section and golden mean (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 Leonardo di ser Piero da Vinci ( pronunciation , April 15, 1452 – May 2, 1519) was an Italian polymath, scientist, mathematician, engineer, inventor, anatomist, painter, sculptor, architect, botanist, musician and writer. Leonardo has often been described as the archetype of the renaissance man, a man whose unquenchable curiosity was equaled 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 The Vitruvian Man is a world-renowned drawing created by Leonardo da Vinci around the year 1487 It is accompanied by notes based on the work of Vitruvius. The drawing, which is in pen and ink on paper, depicts a male figure in two superimposed positions with his arms and legs apart and simultaneously inscribed in a circle and square. The drawing, 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 Alfred North Whitehead, OM was an English mathematician who became a philosopher. He wrote on algebra, logic, foundations of mathematics, philosophy of science, physics, metaphysics, and education. He co-authored the epochal Principia Mathematica with Bertrand Russell (1861-1947), English philosopher and mathematician. Dialogues, June 10, 1943.

Patterns of abstraction may not be directly observable such as patterns in mathematics.

Mathematics

Mathematics Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns.They formulate new conjectures and establish truth by rigorous deduction from appropriately chosen axioms and definitions 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 mannor.

Patterns are common in many areas of mathematics. Recurring decimals A decimal representation of a real number is called a repeating decimal if at some point it becomes periodic: there is some finite sequence of digits that is repeated indefinitely. For example, the decimal representation of 1⁄3 = 0.3333333... (spoken as "0.3 repeating") becomes periodic just after the decimal point, repeating the 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 A fractal is generally "a rough or fragmented geometric shape that can be split into parts, each of which is a reduced-size copy of the whole," a property called self-similarity. Roots of mathematical interest on fractals can be traced back to the late 19th Century, the term however was coined by Benoît Mandelbrot in 1975 and was 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 The science of pattern formation deals with the visible, orderly outcomes of self-organisation and the common principles behind similar patterns can be extremely simple (e.g. Lindenmayer systems for the description of tree A tree is a perennial woody plant. It is most often defined as a woody plant that has many secondary branches supported clear of the ground on a single main stem or trunk with clear apical dominance. A minimum height specification at maturity is cited by some authors, varying from 3 m to 6 m; some authors set a minimum of 10 cm trunk diameter shapes).

Computer Science

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.

Science

In geology, a mineral's crystal structure is composed of a recurring pattern. In fact, this is one of the 5 requirements of a mineral A mineral is a naturally occurring solid formed through geological processes that has a characteristic chemical composition, a highly ordered atomic structure, and specific physical properties. A rock, by comparison, is an aggregate of minerals and/or mineraloids, and need not have a specific chemical composition. Minerals range in composition. Minerals must have a fixed chemical composition in a repeating arrangement, such as a crystal matrix. For a 2-dimensional crystal structure, there are 10 different planar lattices possible. Moving up to 3 dimensions, 32 patterns are possible. These are called bravais lattices.

• Cellular Automata A cellular automaton is a discrete model studied in computability theory, mathematics, theoretical biology and microstructure modeling. It consists of a regular grid of cells, each in one of a finite number of states, such as "On" and "Off". The grid can be in any finite number of dimensions. For each cell, a set of cells
• Crystals In mineralogy and crystallography, a crystal structure is a unique arrangement of atoms in a crystal. A crystal structure is composed of a motif, a set of atoms arranged in a particular way, and a lattice. Motifs are located upon the points of a lattice, which is an array of points repeating periodically in three dimensions. The points can be

See also

• Pattern (sewing) In sewing and fashion design, a pattern is an original garment from which other garments of a similar style are copied, or the paper or cardboard templates from which the parts of a garment are traced onto fabric before cutting out and assembling
• Pattern coin A pattern coin is a coin produced for the purpose of evaluating a proposed coin design, but which was not approved for general circulation. They are often off-metal strikes, to proof standard or piedforts. Patterns are collected by many coin collectors, and although some decide to focus upon them alone, they are generally of interest to all coin
• Pattern (casting) Patterns used in sand casting may be made of wood, metal, plastics or other materials. Patterns are made to exacting standards of construction, so that they can last for a reasonable length of time, according to the quality grade of the pattern being built, and so that they will repeatably provide a dimensionally acceptable casting
• Pattern language Christopher Alexander, an architect and author, coined the term pattern language. He used it to refer to common problems of civil and architectural design, from how cities should be laid out to where windows should be placed in a room. The idea was initially popularized in his book A Pattern Language
• Pedagogical patterns Pedagogical Patterns are high-level patterns that have been recognize in many areas of training and pedagogy such as group work, software design, human computer interaction, education and others. The concept is an extension of pattern languages. In both cases, the patterns seek to foster best practices of teaching
• Pattern (architecture) Pattern in architecture is the idea of capturing architectural design ideas as archetypal and reusable descriptions. The term "pattern" is usually attributed to Christopher Alexander, an Austrian born American architect. The patterns serve as an aid to design cities and buildings. The concept of having collections of "patterns",
• Design pattern A design pattern in architecture and computer science is a formal way of documenting a solution to a design problem in a particular field of expertise. The idea was introduced by the architect Christopher Alexander in the field of architecture, and has been adapted for various other disciplines, including computer science
• Tessellations A tessellation or tiling of the plane is a collection of plane figures that fills the plane with no overlaps and no gaps. One may also speak of tessellations of the parts of the plane or of other surfaces. Generalizations to higher dimensions are also possible. Tessellations frequently appeared in the art of M. C. Escher. Tessellations are seen
• Pattern recognition Pattern recognition is "the act of taking in raw data and taking an action based on the category of the data".[citation needed] Most research in pattern recognition is about methods for supervised learning and unsupervised learning
• Design pattern (computer science)

External links

• Mathematics as a Science of Patterns at Convergence
• Geometric Arts
• Wiki patterns and anti-patterns
• Pattern based desktop art
• Industrial and Decorative Stencils from Stencil Ease
• Patterns, Fractals and Attractors

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