Spatial pattern

Spatialtemporal patterns are patterns that occur in a wide range of natural phenoma and are characterized by a spatial and a temporal patterning. The general rules of pattern formation hold. In contrast to "static", pure spatial patterns, the full complexity of spatiotemporal patterns can only be recognized over time. Any kind of traveling wave is a good example of a spatiotemporal pattern. Besides the shape and amplitude of the wave (spatial part), its time-varying position (and possibly shape) in space is an essential part of the entire pattern.

The distinction between spatial and spatio-temporal patterns in nature is not clear-cut because a static, invariable pattern will never occur in the strict sense. Even rock formations will slowly change on a time-scale of 10,000s up millions of years, therefore the distinction lies in the time scale of change in relation to human experience. Already the snapshot state of a dune will usually be taken as an example of a purely spatial pattern although this is clearly not the case. It is thus apt to say that spatiotemporal patterns in nature are the rule rather than the exception.

Many hydrodynamical systems show s.t. pattern formation:

Any type of reaction-diffusion system that produces spatial patterns will also, due to the time-dependency of both reactions and diffusion, produce spatiotemporal patterns.

Neural networks, both artificial and natural, produce a virtually unbounded variety of s.t. patterns, both in sensory perception, learning, thinking and reasoning as well as in spontaneous activity. It has for example been demonstrated that spiral waves, signatures of many excitable systems can occur in neocortical preparations.

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