User:Evin/3 4 state isotropic rule notation

3 4 state isotropic rule notation is a notation for describing isotropic non-totalistic rules with three or more states. It is based on Hensel notation.

Hensel Notation

Hensel notation describes the relative positions of cells of a certain state as follows:

	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

Rotation IDs

Another important part of 34SIRN is a rotation id. Rotation IDs describe how rotated relative to each other from the configurations shown the two state 2 and state 3 layers are. It is a letter from a-h, representing rotations of 0-315 degrees.

The Notation

The first part consists of two digits from 0-8, which are the count of state 2 and state 4, and the count of state 3 and state 4. Then the next part is the letter for the configuration of state 2 and state 4, followed by the rotation ID, then followed by the configuration of state 3 and state 4.

34SIRN Rules

Then configuration codes for each configuration can be assembled to make a rule. The 34SIRN rulestring takes the form 3, aaa, bbb, ..., fff for three states and 4, aaa, bbb, ..., lll for four states. Just like Hensel notation, configurations can be negated, with configurations automatically negated for three states. Because of the large number of possible strings, the wildcard * can be used to represent any valid value for its position. The letters' use are shown in the following table:

a	0->1
b	0->2
c	1->0	0->3
d	1->2	1->0
e	2->0	1->2
f	2->1	1->3
g	N/A	2->0
h	N/A	2->1
i	N/A	2->3
j	N/A	3->0
k	N/A	3->1
l	N/A	3->2

Extensions

By increasing the number at the beginning, the number of comma-separated strings, and adding more numbers and rotation IDs and letters, 3 4 state isotrpic rule notation extends to any isotropic rule on the Moore neighborhood. By using a rotation ID before each letter, for absolute rotations allows this notation to represent non-isotropic rules as well.

Sample Rules

Brian's Brain

3,2*,,,*,*,