# A Cellular Automaton-Based Heat Equation

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

t+1

T

i,j

4+++++++

t

T

i,j+1

t

T

i,j-1

t

T

i+1,j

t

T

i-1,j

t

T

i+1,j+1

t

T

i+1,j-1

t

T

i-1,j+1

t

T

i-1,j-1

20

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

t

T

i,j

i

th

j

th

t

The initial and boundary conditions are

0

T

i,j

t

T

1,j

t

T

30,j

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.