Pattern formation
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
- Belousov-Zhabotinsky reaction
- Bray-Liebhafsky reaction
- Liesegang rings
- Hantz reactions
- Briggs-Rauscher reaction
physics
- Bénard convection
- Luminous phenomena of a glow discharge
meteorology
- Clouds in rolls / stripes are an example from everyday life.
See also: nephology
biology
Cell differentiation
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
- Symmetry of organisms
- Bilateral symmetry (bilateria),
- Radial symmetry (hollow animals) etc.
- Extremity development
- Segmentation in animals
- Phyllotaxis in plants
- Fingertip pattern ("fingerprints")
- Fur patterns in different mammals (tigers etc.)
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
- Werner Köhler : Pattern formation and pattern recognition. Haug, 1999, ISBN 3-8304-0514-6 .
- Hans Meinhardt among others: Non-linear dynamics, chaos and structure formation. Proceedings of the 6th annual meeting of the Chaos Group. 1997, ISBN 3-929115-94-8 .
- Andreas Bresinsky, Christian Körner, Joachim W. Kadereit, Gunther Neuhaus, Uwe Sonnewald: Textbook of botany for universities . 36th edition. Spectrum, 2008, ISBN 978-3-8274-1455-7 , p. 427.
- James D. Murray : Mathematical Biology II: Spatial Models and Biomedical Applications. 3. Edition. Springer, Berlin 2003, ISBN 0-387-95228-4 (English).
- Hans Meinhardt: Construction and dismantling of patterns in biology. In: Biology in Our Time. 2001 (PDF).
- Werner Ebeling , Jan Freund, Frank Schweitzer: Complex structures, entropy and information. Teubner, 1998, ISBN 3-8154-3032-1 .
Web links
- Botany online: growth and differentiation - pattern formation
- D. Pongs: Experimental Approaches to Structure Formation. Westphalian Wilhelms University, Münster 2002.