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Patterns in nature are visible regularities of form found in the natural world. These patterns recur in different contexts and can sometimes be modelled mathematically. Natural patterns include symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes. [1] Early Greek philosophers studied pattern, with Plato ...
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 ...
A logarithmic spiral, equiangular spiral, or growth spiral is a self-similar spiral curve that often appears in nature. The first to describe a logarithmic spiral was Albrecht Dürer (1525) who called it an "eternal line" ("ewige Linie"). [1][2] More than a century later, the curve was discussed by Descartes (1638), and later extensively ...
Many patterns in nature are formed by cracks in sheets of materials. These patterns can be described by Gilbert tessellations, [85] also known as random crack networks. [86] The Gilbert tessellation is a mathematical model for the formation of mudcracks, needle-like crystals, and similar structures.
The Chemical Basis of Morphogenesis. Turing's paper explained how natural patterns, such as stripes, spots, and spirals, like those of the giant pufferfish, may arise. " The Chemical Basis of Morphogenesis " is an article that the English mathematician Alan Turing wrote in 1952. [ 1] It describes how patterns in nature, such as stripes and ...
The recursive nature of some patterns is obvious in certain examples—a branch from a tree or a frond from a fern is a miniature replica of the whole: not identical, but similar in nature. Similarly, random fractals have been used to describe/create many highly irregular real-world objects, such as coastlines and mountains.
Symmetry in biology refers to the symmetry observed in organisms, including plants, animals, fungi, and bacteria. External symmetry can be easily seen by just looking at an organism. For example, the face of a human being has a plane of symmetry down its centre, or a pine cone displays a clear symmetrical spiral pattern.
Common and special causes are the two distinct origins of variation in a process, as defined in the statistical thinking and methods of Walter A. Shewhart and W. Edwards Deming. Briefly, "common causes", also called natural patterns, are the usual, historical, quantifiable variation in a system, while "special causes" are unusual, not ...