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.