A Cellular Automaton-Based Heat Equation

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This Demonstration shows unsteady-state conduction of heat in two dimensions by means of a coupled-map lattice, for example a continuous-state cellular automaton. The heat transfer is governed by



where represents the temperature in degrees Celsius of the cell at the time step.

The initial and boundary conditions are




which are relatively simple, but can be adjusted in accordance with the problem at hand. The result approaches the solution of the classic PDE-based heat equation for unsteady heat conduction.


Contributed by: Jan Baetens (March 2011)
Open content licensed under CC BY-NC-SA



The CA-based heat equation was formulated in:

J. L. Schiff, Cellular Automata: A Discrete View of the World, New York: Wiley, 2008.

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