Spatial patterns
From NECSIWiki
Patterns in space and time arise because of the interactions between elements of a system. How and which patterns are formed are central questions in the study of complex systems.
One of the central quesetions about how patterns form is whether they form when a system is in equilibrium or only when the system is not in equilibrium.
The first paper to discuss mathematically the formation of patterns was by Alan Turing. The question addressed by this paper was how patterns might form. Diffusion causes a system to become more homogeneous. This paper showed how a system that had reactions in addition to diffusion could create patterns. When patterns are modelled by differential equations they are often called Turing patterns
Spatial systems are also often modeled by Cellular Automata, which can be designed to have patterns.
Pattern formation is an example of symmetry breaking, the process by which a system starts with a symmetry and by the dynamics of how it works the symmetry is no longer there. In this case the symmetry is that the underlying space is the same everywhere, but then once the pattern forms it is not the same everywhere.
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[edit] Spatial Patterns and Hierarchy Theory
Another aspect of spatial patterns is dealt with in hierarchy theory, in particular in Scale hierarchy theory.
[edit] References:
- Salthe, S.N., 1985. Evolving Hierarchical Systems. Columbia UP.
- Salthe, S.N., 2002. General Systems Bulletin 31: 13-17.
[edit] Pattern Formation in Developmental Biology
The development of a multicellular biological organism from a fertilized egg or seed is a dramatic example of pattern formation. While peopel often talk about the "DNA blueprint," there is no picture in the DNA that shows how to construct a biological organism. Much of the information about the organism is surely in the genome. However, the process by which it happens is a process of pattern fomation.
[edit] References:
- A.M. Turing. 1952. The Chemical Basis of Morphogenesis. Phil. Trans. Royal Society, vol. B237, pp. 37 - 72.
- J.D. Murray, Mathematical Biology. Springer-Verlag,
- L.A. Segel, Modeling dynamic phenomena in molecular and cellular biology. Cambridge University Press, 1984
- Y. Bar-Yam, Dynamics of Complex Systems, Perseus, 1997, Chap. 7
[edit] Pattern Formation in Population Biology
The formation of patterns in spatial populations of biological organisms is a subject of recent interest.
