Resource type
Thesis type
(Thesis) M.Sc.
Date created
2006
Authors/Contributors
Author: Yi, Ling Yu
Abstract
A cellular automaton (CA) is a discrete microscopic dynamical system widely used to investigate and understand the mechanisms of complex systems such as reaction-diffusion systems based on cell-cell interactions. We introduce two CA models for Turing-type pattern formation. These are a moving average CA and lattice-gas CA. For a moving average CA, the construction of the local CA rules from the reaction-diffusion partial differential equations relies on a moving-average procedure to implement the diffusive step and a probabilistic table lookup for the reactive step. We apply this method to the 2D Brusselator system. The corresponding 11-state CA model is able to capture the Hopf and Turing birfucation. For a lattice-gas CA, we introduce a modified reaction rule for an activator-inhibitor system and combine it with the propagation rule and shuffling rule. A variety of dynamics arise in this LGCA model. Numerical simulations of both CA models are presented and analyzed.
Document
Copyright statement
Copyright is held by the author.
Scholarly level
Language
English
Member of collection
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