Pattern formation
Pattern formation is occurring in different contexts temporary dynamic process, in which independently form periodic patterns or structures after previously an initially spatially homogeneous state has become unstable, thus has been a phase transition.
Pattern formation can occur spatially, temporally, or spatially and temporally. Retrieved from " structures " instead of " patterns " are used, typically when the patterns occur spatially and non-volatile, ie when temporary spatial patterns stabilize.
- 2.3.1 Cell Differentiation
- 2.3.2 Anatomy
- 2.3.3 Neural activation patterns
- 2.4.1 Ecology
Principle
In most cases the initial symmetry breaking is triggered by changing a parameter in a nonlinear system. Since pattern formation occurs in a narrow sense and spontaneously without any external influence, it is partly based on the principles of self-organization. Ilya Prigogine suggested that order emerges from chaos ( disorder ) on a path of successive bifurcations. In developmental biology, the emergence of complex tissue structures is called to form a pattern that determine the spatial and temporal cell fate.
The formation of an ordered state is associated with a local decrease in entropy compared to a reference state of the same energy. The order is subject to rules. So patterns can only occur automatically when the total entropy still increases. Only within the considered system increases the entropy from locally. A person has, for example, eat food in order to grow and maintain itself. Man as dissipative ( energieentwertende / entropieerzeugende ) structure decomposes it more structure ( Nahrung. ..) than it forms. In this way, the automatic generation of structures is not in contradiction to the second law of thermodynamics.
See also: reaction-diffusion equations, feedback, autocatalysis, Dissipative Systems (dissipation )
Examples
Chemistry
- Belousov -Zhabotinsky reaction
- Bray- Liebhafsky reaction
- Briggs - Rauscher reaction
Physics
- Bénard convection
- Luminous phenomena of a glow discharge
Meteorology
- Clouds in rolls / stripe patterns are an example from everyday life.
See also: Nephologie
Biology
Cell differentiation
Even cell differentiation in a tissue subject to pattern formation processes. Here, a slow or non -diffusing activator is stochastically formed periclinal cells in a tissue layer, which his own education autocatalytically amplified and at the same time induces the formation of a rapidly diffusing inhibitor. This prevents inhibitor, due to the greater range in the vicinity of the "activated" cell Aktivatorbildung and thus a differentiation of the neighboring cell.
Anatomy
With the structure formation of ( individual) organisms and their organs, known as morphogenesis, the principles of pattern formation play a central role. In this play, the concrete individual components (genes, hormones), is not so important as the autocatalytic effect of the subsystems. Pattern formation is inter alia responsible for
- Symmetry of the organisms Bilateral symmetry ( bilaterians ), Radiärsymmetrie ( coelenterates ), etc.
Neural activation patterns
Each stimulus excites the central nervous system for a specific excitation pattern in certain aspects of the stimulus pattern reflects (see eg tonotopy ). Without this coordinated spatio- temporal activity pattern recognition would be ( in the stimulus source) impossible. Pattern formation and recognition are so closely linked in the brain together.
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