A Cellular Automaton-Based Heat Equation

time step

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

t

T

i,j

represents the temperature in degrees Celsius of the

i

th

j

cell at the

th

t

time step.

The initial and boundary conditions are

0

T

i,j

=10°C

,

t

T

1,j

=-22°C

,

t

T

30,j

=22°C

,

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.