User:Apple Bottom/Incubator/Swedish notation

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Swedish notation[note 1] is a system for encoding non-isotropic Life-like cellular automata in a manner that is more intuitive than MAP strings.[1]

Swedish notation assigns a single letter to each of the eight major compass directions, as follows; "vänster" and "höger" are Swedish for "left" and "right":

l
(left)
n
(north)
r
(right)
w
(west)
e
(east)
v
(vänster)
s
(south)
h
(höger)

Each possible neighborhood configuration with n < 5 live cells is represented as a group of letters indicating which cells are live (in any order); for n ≥ 5 live cells, the letters instead represent the dead cells, to keep the overall notation shorter and more intuitively understood. For example:

Neighborhood 2a.png Neighborhood 2a rotated.png Neighborhood 3k.png Neighborhood 5a.png Neighborhood 6c.png Neighborhood 7c.png
2(ln) 2(re) 3(wnh) 5(lnw) 6(lr) 7(l)

Different neighborhood configurations with the same number n of live cells are separated with commas and grouped along with the respective birth (Bn) or survival (Sn) condition:

Neighborhood 2a.png Neighborhood 2a rotated.png Neighborhood 3k.png Neighborhood 5a.png Neighborhood 6c.png Neighborhood 7c.png
B2(ln,re)3(wnh)5(lnw)6(lr)7(l)

As with Hensel notation for isotropic non-totalistic Life-like cellular automata, conditions can be negated by prefixing them with a minus sign. For example, a cellular automaton in which dead cells get born if they have two live neighbors, unless those neighbors happen to be located southeast (h) and north (n) of a cell, would include "B2(-hn)" as part of its rulestring in Swedish notation.

If all possible neighborhood configurations lead to the birth or survival of a cell, they do need to be listed individually; for example, "B1" is equivalent to "B1(l,n,r,w,e,v,s,h)".

Comparison to MAP strings

Swedish notation rulestrings are, on average, longer than the MAP strings describing the same cellular automata, but can be understood, created and read more easily than MAP strings by humans.

Also see

Notes

  1. The name "Swedish notation" refers to the use of "vänster" and "höger" for the backward diagonal compass directions, but is also a pun on "Polish notation" and "Hungarian notation".

References

  1. Apple Bottom. Re: Thread for basic questions (discussion thread) at the ConwayLife.com forums