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