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Turing Patterns

Irving R. Epstein and John A. Pojman

in An Introduction to Nonlinear Chemical Dynamics: Oscillations, Waves, Patterns, and Chaos

Published in print:
1998
Published Online:
November 2020
ISBN:
9780195096705
eISBN:
9780197560815
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195096705.003.0020
Subject:
Chemistry, Physical Chemistry

In the first chapter of this book, we noted the “dark age” of nearly forty years separating the work of Bray and Lotka in the early 1920s and the discovery of the BZ reaction in the late 1950s. ... More


Self-Assembly and Beyond

Troy Shinbrot

in Biomedical Fluid Dynamics: Flow and Form

Published in print:
2019
Published Online:
June 2019
ISBN:
9780198812586
eISBN:
9780191850721
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198812586.003.0013
Subject:
Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

Effects of combining reaction with diffusion are examined, and the resulting self-assembly of ordered patterns is overviewed. Turing patterns and limit cycle oscillations are shown to result from ... More


Turing Patterns in Ferroelectric Domains: Nonlinear Instabilities

J. F. Scott

in Domain Walls: From Fundamental Properties to Nanotechnology Concepts

Published in print:
2020
Published Online:
October 2020
ISBN:
9780198862499
eISBN:
9780191895319
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198862499.003.0008
Subject:
Physics, Condensed Matter Physics / Materials, Theoretical, Computational, and Statistical Physics

This chapter outlines how ferroelectric domain patterns link to various, cross-disciplinary, fundamental instabilities. It starts by highlighting the startling resemblance between Turing patterns and ... More


Continuous-Valued Cellular Automata in Two Dimensions

Rudy Rucker

in New Constructions in Cellular Automata

Published in print:
2003
Published Online:
November 2020
ISBN:
9780195137170
eISBN:
9780197561652
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/9780195137170.003.0016
Subject:
Computer Science, Systems Analysis and Design

We explore a variety of two-dimensional continuous-valued cellular automata (CAs). We discuss how to derive CA schemes from differential equations and look at CAs based on several kinds of ... More


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