Totalistic Cellular Automaton with Rule 935912 r = 1, k = 4

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.

The totalistic cellular automaton (CA) with rule number 935912 (, ) keeps the initial four colors until the end of the evolution. It is a class IV CA that has random behavior with some nested structures. There are clearly some repetitive patterns in the evolution that create stripes and walls, and some structures with gliders. Mouseover the image to see its evolution from one cell as the initial condition. The time series shows the dynamical behavior of each CA color with increasing steps.


The rule number 935912 was found by a brute-force search that ordered all the totalistic CA ( in total) with four colors () and one neighborhood () according to complexity and by a human visual inspection of the most complex cases.

The search algorithm runs in a Linux systems with an Intel i7 processor with 8 cores CPU and Nvidia 128 cores GPU, using the parallel processing capabilities of Mathematica. The combination of colors is important to highlight the characteristics of the evolution as well to come up with an interesting texture.


Contributed by: Daniel de Souza Carvalho (July 2011)
Open content licensed under CC BY-NC-SA



New Kind of Science Summer School 2011


[1] S. Wolfram, A New Kind of Science, Champaign, IL: Wolfram Media, Inc. , 2002.

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.