Isotropic non-totalistic rule

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
	File:Neighborhood 0.png								File:Neighborhood 8.png
c (corner)			File:Neighborhood 2c.png	File:Neighborhood 3c.png	File:Neighborhood 4c.png	File:Neighborhood 5c.png	File:Neighborhood 6c.png	File:Neighborhood 7c.png
e (edge)		File:Neighborhood 1e.png	File:Neighborhood 2e.png	File:Neighborhood 3e.png	File:Neighborhood 4e.png	File:Neighborhood 5e.png	File:Neighborhood 6e.png	File:Neighborhood 7e.png
k (knight)			File:Neighborhood 2k.png	File:Neighborhood 3k.png	File:Neighborhood 4k.png	File:Neighborhood 5k.png	File:Neighborhood 6k.png
a (adjacent)			File:Neighborhood 2a.png	File:Neighborhood 3a.png	File:Neighborhood 4a.png	File:Neighborhood 5a.png	File:Neighborhood 6a.png
i			File:Neighborhood 2i.png	File:Neighborhood 3i.png	File:Neighborhood 4i.png	File:Neighborhood 5i.png	File:Neighborhood 6i.png
n			File:Neighborhood 2n.png	File:Neighborhood 3n.png	File:Neighborhood 4n.png	File:Neighborhood 5n.png	File:Neighborhood 6n.png
y				File:Neighborhood 3y.png	File:Neighborhood 4y.png	File:Neighborhood 5y.png
q				File:Neighborhood 3q.png	File:Neighborhood 4q.png	File:Neighborhood 5q.png
j				File:Neighborhood 3j.png	File:Neighborhood 4j.png	File:Neighborhood 5j.png
r				File:Neighborhood 3r.png	File:Neighborhood 4r.png	File:Neighborhood 5r.png
t					File:Neighborhood 4t.png
w					File:Neighborhood 4w.png
z					File:Neighborhood 4z.png

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.

Soup-searching non-totalistic rules

Adam P. Goucher's apgsearch was modified to support non-totalistic rules by Aidan F. Pierce on December 17, 2015. Catagolue gained the ability to census non-totalistic rules in late January 2016.

See also

• Generations
• MAP
• Larger than Life

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)