# Isotropic non-totalistic Life-like cellular automaton

**Non-totalistic Life-like cellular automata** are a generalization of Life-like cellular automata in which the transition function considers not just the number of cells in a given cell's neighborhood but also their alignment.

Non-totalistic rules are described using Hensel notation, an extension of B/S notation developed by Alan Hensel additionally describing allowed or forbidden configurations. Each digit in the rule's birth and survival conditions is followed by an optional suffix, with each allowed configuration described by a specific letter; a minus sign may be used to forbid configurations rather than allow them. If no configurations are specified, all are considered to be allowed, as in the totalistic case.

The following table summarizes all possible neighborhood configurations:

0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |
---|---|---|---|---|---|---|---|---|---|

c (corner) | |||||||||

e (edge) | |||||||||

k (knight) | |||||||||

a (adjacent) | |||||||||

i | |||||||||

n | |||||||||

y | |||||||||

q | |||||||||

j | |||||||||

r | |||||||||

t | |||||||||

w | |||||||||

z |

For instance, B2-a/S12 (the "Just Friends" rule) indicates that a live cell will survival on 1 or 2 neighbors, or a dead cell get born on 2 neighbors, except when they are adjacent.

## External links

- Alan Hensel. "Table of non-totalistic neighborhoods". Retrieved on 2016-06-12.
- Alan Hensel. "Rule notation". Retrieved on 2016-06-12. (note that the table on this page describes an earlier version of Hensel notation that has fallen into disuse)