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.
Keywords: pattern formation, fluid flow, coupled oscillators, cellular automata, reaction-diffusion models, fractal dimension, self-organized criticality
Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.
Please, subscribe or login to access full text content.
If you think you should have access to this title, please contact your librarian.
To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .