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The solutions of reaction–diffusion equations display a wide range of behaviours, including the formation of travelling waves and wave-like phenomena as well as other self-organized patterns like stripes, hexagons or more intricate structure like dissipative solitons. Such patterns have been dubbed "Turing patterns". [1]
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.
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.
In chemistry, periodic trends are specific patterns present in the periodic table that illustrate different aspects of certain elements when grouped by period and/or group. They were discovered by the Russian chemist Dmitri Mendeleev in 1863.
SMILES arbitrary target specification (SMARTS) is a language for specifying substructural patterns in molecules.The SMARTS line notation is expressive and allows extremely precise and transparent substructural specification and atom typing.
This behavior can be studied through the analysis of a chaotic mathematical model or through analytical techniques such as recurrence plots and Poincaré maps. Chaos theory has applications in a variety of disciplines, including meteorology , [ 9 ] anthropology , [ 16 ] sociology , environmental science , computer science , engineering ...
A composite rhythm is the durations and patterns (rhythm) produced by amalgamating all sounding parts of a musical texture. In music of the common practice period , the composite rhythm usually confirms the meter , often in metric or even-note patterns identical to the pulse on a specific metric level.
Since the diffraction pattern can be seen as a two-dimensional projection of reciprocal crystal lattice, the pattern can be used to measure lattice constants, specifically the distances and angles between crystallographic planes. The lattice parameters are typically distinctive for various materials and their phases which allows to identify the ...