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A Cellular Automaton-Based Heat Equation
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.



The CA-based heat equation was formulated in:
J. L. Schiff, Cellular Automata: A Discrete View of the World, New York: Wiley, 2008.


"A Cellular Automaton-Based Heat Equation" from The Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/ACellularAutomatonBasedHeatEquation/
Contributed by: Jan Baetens
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