# Other Cellular Automata Rules

Introduction |
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.

**See also:**
definitions,
structure,
search methodologies,
other rules,
news,
credits,
links,
site map,
search,
expanded search,
search help,
downloads.

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Copyright © 1997, 1998, 1999, 2013, 2014 by Mark. D. Niemiec.
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This page was last updated on
*2015-02-19*.