Pattern Formation and Spatiotemporal Chaos
When a dynamical system has significant spatial extent, its nonlinear dynamics can lead to the spontaneous formation of spatial patterns. Such systems provide models for how nature might have developed ordered, spatial structures from disordered states. Examples are given from fluid flow, transport models, coupled-oscillator modes, cellular automata, transport models, and reaction-diffusion systems. Diffusion-limited aggregation, viscous fingering, and dielectric breakdown provide further examples of pattern formation. Fractal structures make another appearance in this new context. This chapter also explores the somewhat controversial topic of self-organized criticality which has been put forward as an explanation for the occurrence of fractal structures in nature.
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