Simulating Spatial Partial Differential Equations with Cellular Automata

Abstract-- Spatial partial differential equations are commonly used to describe systems of biological entities, such as patterns created by desert vegetation and biovermiculation growth, the type of life that could hypothetically live within the caves of Mars. These equations can be transformed into cellular automata models, which have the benefit of being easily simulated, highly parallelizable, and change the perspective of the model to a local view. This paper discusses how to accomplish this transformation using two methods. The transformation methods are then analyzed using the Ztransform, resulting in guidelines for optimum discretization of space and time in order to achieve convergence and quicker simulations.

• Type: Journal
• Year: 2009
• Where: BIOCOMP
• Authors: Brian Strader, Keith E. Schubert, Ernesto Gomez, Jane Curnutt, Penelope Boston
• Keywords: BIOCOMP 2009, Bioinformatics, Cellular Automata Models, Desert Vegetation, Optimum Discretization