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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 ]
It describes how patterns in nature, such as stripes and spirals, can arise naturally from a homogeneous, uniform state. The theory, which can be called a reaction–diffusion theory of morphogenesis, has become a basic model in theoretical biology. [2] Such patterns have come to be known as Turing patterns.
Three examples of Turing patterns Six stable states from Turing equations, the last one forms Turing patterns. 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.
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.
Historic recurrence is the repetition of similar events in history. [a] [b] The concept of historic recurrence has variously been applied to overall human history (e.g., to the rises and falls of empires), to repetitive patterns in the history of a given polity, and to any two specific events which bear a striking similarity. [4]
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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 science of pattern formation deals with the visible, (statistically) orderly outcomes of self-organization and the common principles behind similar patterns in nature. In developmental biology , pattern formation refers to the generation of complex organizations of cell fates in space and time.