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Natural patterns include spirals, meanders, waves, foams, tilings, cracks, and those created by symmetries of rotation and reflection. Patterns have an underlying mathematical structure; [2]: 6 indeed, mathematics can be seen as the search for regularities, and the output of any function is a mathematical pattern. Similarly in the sciences ...
If his patterns are more permanent than theirs, it is because they are made with ideas. [22] G. H. Hardy, 1940. Mathematics is the art of giving the same name to different things. [10] Henri Poincaré. Mathematics is the science of skillful operations with concepts and rules invented just for this purpose.
A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called tiles, with no overlaps and no gaps. In mathematics, tessellation can be generalized to higher dimensions and a variety of geometries. A periodic tiling has a repeating pattern. Some special kinds include regular tilings with regular ...
The Turing pattern is a concept introduced by English mathematician Alan Turing in a 1952 paper titled "The Chemical Basis of Morphogenesis" which describes how patterns in nature, such as stripes and spots, can arise naturally and autonomously from a homogeneous, uniform state. [1][2] The pattern arises due to Turing instability which in turn ...
Mathematics is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study ...
Pattern theory, formulated by Ulf Grenander, is a mathematical formalism to describe knowledge of the world as patterns.It differs from other approaches to artificial intelligence in that it does not begin by prescribing algorithms and machinery to recognize and classify patterns; rather, it prescribes a vocabulary to articulate and recast the pattern concepts in precise language.
Cutaway of a nautilus shell showing the chambers arranged in an approximately logarithmic spiral. In mathematics, a spiral is a curve which emanates from a point, moving farther away as it revolves around the point. [1][2][3][4] It is a subtype of whorled patterns, a broad group that also includes concentric objects.
Nonlinear dynamics. Game theory. v. t. e. In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. [1][2] Nonlinear problems are of interest to engineers, biologists, [3][4][5] physicists, [6][7] mathematicians, and many other scientists ...