Elementary Cellular Automaton Process Visualization

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

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

Elementary cellular automata evolve a vector of bits by processing overlapping three element neighborhoods according to an eight-bit rule.


The visualization shows the one-bits in the history by corresponding gray cuboids in a plane. A second plane is used to represent the parallel lookup operations which compute the next state vector. This second plane shows multiple representations of the one-bits in the rule number together with three shifted representations of the one-bits in the state vector which is currently processed. The one-bits of the computed new state vector are shown at the intersection of the history plane and the processing plane.

The lookup procedure is illustrated by color-coding. The cubes representing the three neighborhood one-bits are colored according to these three bits by interpreting these bits as RGB intensities. The cubes which represent the rule bits are color-coded too, their colors however correspond to the bits which address that particular one-bit in the rule number. The lookup matches the colors of the neighborhood with the colors in the rule. The computed new bit is a one-bit if the color of the neighborhood is among the colors of the rule; it is a zero-bit if there is no cube in the rule representation which has that color.


Contributed by: Michael Schreiber (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.