# Totalistic K3 R 1/2 Cellular Automata

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.

Totalistic cellular automata depend only on the sum of the values of the cells in their neighborhood on the previous step. Range 1/2 cellular automata depend only on the center cell and the cell just to its left on the previous step. Here, 3-color range 1/2 totalistic cellular automata are investigated for all possible single-cell "seeds" on any uniform "background", and for a sample of random initial conditions.

Contributed by: Jason Cawley (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Simple nested patterns are common.

Notice that the patterns can grow only to the right, due to range 1/2.

Behaviors seen in some rules are repeated in others that are equivalent under a color rotation.

More complex behaviors are seen from simple initials in rules 38 and 61, for example.

Some rules, like rule 100, show particularly complex behavior from random initial conditions.

Rule 106 shows simple particles from simple initials, but complex interactions among multiple particle types from random initial conditions.

## Permanent Citation