# Other Cellular Automata Rules

## Introduction

All the rules described here are similar to Life, with some minor changes. Unless otherwise noted, they all are all two state (i.e. cells are dead or alive), totalistic (i.e. a cell's state is determined solely on its own state and the sum of its neighbors without regard to their relative positions), and use a Moore neighborhood (i.e. a two-dimensional square lattice in which every cell's neighborhoods consists of the 4 orthogonally adjacent and 4 diagonally adjacent cells).

## Rules

• B3/S23 (Conway's Game of Life): This rule has birth on 3 neighbors, and survival on 2 or 3 neighbors. This is one of the most interesting, and most widely studied two-dimensional cellular automata, and the subject of most of these pages.
• Multi-colored Life: This describes several enhanced multi-state versions of Life, where cells are born and die the same way as in Life, but there are multiple living states (typically indicated by different colors) that supply additional information and complexity.
• B34/S34 (3/4 Life): This rule has both birth and survival on 3 or 4 neighbors. There was a fairly extensive discussion of this rule in the Lifeline newsletter in the 1970s. It is also fairly interesting, but many patterns expand infinitely, making it harder to work with.
• B2/S2 (2/2 Life): This rule has both birth and survival on 2. Patterns are extremely volatile, and it is difficult to make them not expand without limit.
• Niemiec's Rules: This is actually several closely-related rules. While the birth conditions are totalistic (and, in fact, the same as Life's), the survival conditions are not totalistic - i.e. they depend not only on the number of neighbors, but also their relative positions. Birth occurs on any 3 neighbors, while survival occurs on 2-4 neighbors that are orthogonally connected to the original cell (i.e. diagonal neighbors are allowed only if they are themselves adjacent to one or two orthogonal neighbors). Most common patterns are shared by all variants. Some characteristics of these rules rule are that most useful patterns are or contain ominos, ad there are 4 natural spaceships, all of different velocities, several simple guns and puffers, and a natural replicator.