Geometric and Stochastic Analysis of Reaction-Diffusion Patterns

Abstract

After Turing’s ingenious work on the chemical basis of morphogenesis fifty years ago, reactiondiffusion patterns have been extensively studied in terms of modelling and analysis of pattern formations (in both chemistry and biology), pattern growing in complex laboratory environments, and novel applications in computer graphics. A fundamental question that remains unanswered in the literature is what one precisely means by (reaction-diffusion) patterns. Most patterns have only been discovered, identified, or explained by human vision and human intelligence. Inspired by the recent advancement in mathematical image and vision analysis (Miva), the current paper develops both geometric and stochastic tools and frameworks for identifying, classifying, and characterizing common reaction-diffusion patterns and pattern formations. In essence, it presents a data mining theory for the scientific simulations of reaction-diffusion patterns, or various analytical tools for the automatic characterization of generic complex patterns by artificial intelligence.

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Cite this paper

@inproceedings{ShenGeometricAS, title={Geometric and Stochastic Analysis of Reaction-Diffusion Patterns}, author={Jianhong Shen and Yoon Mo Jung} }