Self-complementary: Difference between revisions
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A (totalistic) [[rule]] is said to be '''self-complementary''' if it remains unchanged under [[black/white reversal]], i.e. if a pattern composed of live [[cell]]s in a dead universe behaves the same as an equivalent pattern composed of dead cells in a live universe. | A (totalistic) [[rule]] is said to be '''self-complementary''' if it remains unchanged under [[black/white reversal]], i.e. if a [[pattern]] composed of live [[cell]]s in a dead [[universe]] behaves the same as an equivalent pattern composed of dead cells in a live universe. | ||
A self-complementary rule's birth conditions completely determine its survival conditions, and vice versa, but no other constraints exist; as such there are 2<sup>9</sup> = 512 distinct self-complementary totalistic rules. | A self-complementary rule's birth conditions completely determine its survival conditions, and vice versa, but no other constraints exist; as such there are 2<sup>9</sup> = 512 distinct self-complementary totalistic rules. | ||
Revision as of 21:38, 1 July 2016
A (totalistic) rule is said to be self-complementary if it remains unchanged under black/white reversal, i.e. if a pattern composed of live cells in a dead universe behaves the same as an equivalent pattern composed of dead cells in a live universe.
A self-complementary rule's birth conditions completely determine its survival conditions, and vice versa, but no other constraints exist; as such there are 29 = 512 distinct self-complementary totalistic rules.
Examples
- Main article: List of self-complementary rules
The most well-known and well-investigated self-complementary rule is Day & Night (B3678/S34678).