LifeWiki:FAQ/Hensel notation

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The Hensel notation is a rulestring notation for defining isotropic two-state rules that use range-1 Moore neighbourhood.

Examples

Here are a few examples of this notation:

What do all the letters mean?

This table lists notations for all possible 3 × 3 neighbourhood configurations. It can also be found in Golly help, under Help → Algorithms → QuickLife → Non-totalistic rules.

0 1 2 3 4 5 6 7 8
—
(no letter)
c
(corner)
e
(edge)
k
(knight)
a
(adjacent)
i
n
y
q
j
r
t
w
z

Why do I see things like "B2x" or "S4v" in old discussions?

In the past, there were several slightly differing variants of the notation; differences included using letter "v" instead of "n", and swapping the meaning of letters "y" and "r".

The modification of gencols by Paul Tooke supports searching isotropic rules, and uses a variant of Hensel notation where "v" is used instead of "n".

What is the rarest condition? What isotropic rule is closest to Life?

When evolving large random soups, the rarest 3 × 3 "window" of cells is S4c: 

o.o  S4c
.o.
o.o

Second rarest neighbourhood condition is B8: 

ooo  B8
o.o
ooo

Third rarest neighbourhood condition is S6i: 

ooo  S6i
.o.
ooo

This suggests that isotropic rules B3/S234c, B38/S23, B3/S236i should be fairly "similar" to Life. (The overall behaviour of those rules is indeed similar to that of Life; nevertheless, each rule supports some interesting alien objects that do not exist in plain Life.)

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