A Cellular Automaton-Based Heat Equation

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

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]

Contributed by: Jan Baetens (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

The CA-based heat equation was formulated in:

J. L. Schiff, Cellular Automata: A Discrete View of the World, New York: Wiley, 2008.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send