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