Pattern formation

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Pattern formation is a time-limited dynamic process that occurs in different contexts , in which periodic patterns or structures form independently after an originally spatially homogeneous state has become unstable , i.e. a phase transition has taken place.

Pattern formation can take place in space, time, or space-time. One speaks of “structures” instead of “patterns”. d. As a rule, if the patterns occur spatially and non-volatile, i.e. H. when temporary spatial patterns stabilize.

Principles

Usually the initial symmetry breaking is triggered by changing a parameter in a non-linear system . Since pattern formation in the narrower sense happens spontaneously and without external influence, it is based in part on the principles of self-organization . Ilya Prigogine suggested that order emerges from chaos ( disorder ) along a path of successive bifurcations . In developmental biology , pattern formation refers to the formation of complex tissue structures that determine the spatial and temporal cell fate .

The development of a state of order is associated with a local reduction in entropy compared to a reference state of the same energy. Order is subject to rules. Patterns can only arise automatically if the overall entropy nevertheless increases. Entropy only decreases locally within the system under consideration. A person must z. B. Eat food to grow and sustain yourself. The human being as a dissipative (energy devaluing / entropy generating) structure decomposes more structure (food ...) than he builds up. In this way, the automatic formation of structures does not contradict the 2nd law of thermodynamics .

See also : reaction diffusion equations , feedback , autocatalysis , dissipative systems ( dissipation )

Examples

chemistry

physics

meteorology

  • Clouds in rolls / stripes are an example from everyday life.

See also: nephology

biology

Cell differentiation

A (medium green) "activated" cell, a activator, i inhibitor, I (dark green) inhibitor cell, C (light green) tissue cell, the diagram shows the activity of activator and inhibitor depending on the cell (activator cell or inhibitor cell)

Even the cell differentiation in a tissue is subject to pattern formation processes. In this case, an activator that diffuses slowly or not at all is formed stochastically periclinically in cells of a tissue layer, which autocatalytically intensifies its own formation and thus simultaneously induces the formation of a more rapidly diffusing inhibitor. Due to the greater range, this inhibitor prevents activator formation in the vicinity of the "activated" cell and thus differentiation of the neighboring cell.

anatomy

In the structure formation of (single) organisms and their organs, the so-called morphogenesis , the principles of pattern formation play a central role. The specific individual components (genes, hormones) do not play as big a role as the autocatalytic effect of the subsystems. Pattern formation is u. a. responsible for the

Neural activation patterns

Every stimulus excites a certain stimulation pattern in the central nervous system , which in certain aspects reflects the stimulus pattern (see e.g. tonotopia ). Without this coordinated spatio-temporal activity, pattern recognition (in the stimulus source) would be impossible. Pattern formation and recognition are therefore closely linked to one another in the brain.

See also: action potential , circadian rhythm

Hormonal rhythms

See also: menstrual cycle

ecology

See also: predator-prey model

Modeling

See also: Turing mechanism , L-systems , cellular automaton , FitzHugh-Nagumo model , Swift-Hohenberg equation , reaction diffusion equation

literature

Web links