Isotropic non-totalistic rule

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Non-totalistic Life-like cellular automata are a generalization of Life-like cellular automata in any transition function which is isotropic (that is, invariant under rotations and reflections) is allowed.

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.

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.

This notation has the following symmetry: For any letter x and number n≠4, nx is defined if and only x(8-n) is defined and moreover x(8-n) is the complement (change live cells to dead and dead cells to live; ignore the center cell) of xn.

The following table describes all possible neighborhood configurations:

0 1 2 3 4 5 6 7 8
(no
letter)
File:Neighborhood 0.png File:Neighborhood 8.png
c
(corner)
Neighborhood 1c.png 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

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.[1] Catagolue gained the ability to census non-totalistic rules in late January 2016.[2]

See also

References

  1. Aidan F. Pierce (December 17, 2015). "Re: Hacking apgsearch". ConwayLife.com forums. Retrieved on June 12, 2016.
  2. Adam P. Goucher (January 21, 2016). "Re: apgsearch v2.2". ConwayLife.com forums. Retrieved on June 12, 2016.

External links