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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

[more]

,

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.

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

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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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