Replicating Patterns in 2D Binary Cellular Automata with the Parity Rule

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 simulates the dynamics of 2D binary cellular automata with the "parity" rule, using automatic real-time updating. To start or stop the simulation, click the "run simulation" checkbox.


Each cell counts how many cells within its Moore neighborhood (including itself) is "on". If that number is odd, the cell turns "on" at the next time step; otherwise it turns "off". A simulation starting with a single "on" cell shows the proliferation of the state over the space in a recursive way, creating a 3D Sierpinski gasket in spacetime. You can also place a small "A" by clicking "place 'A'" button or create your own initial configuration by clicking anywhere in the CA space. The information about the initial pattern won't be lost in this CA, and you will see the same pattern replicate and reappear from time to time as the simulation goes on.


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




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.