Self-complementary: Difference between revisions

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{{Glossary}}
{{Glossary}}
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.
An (outer-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 outer-totalistic rules.


==Examples==
==Examples==
<!-- {{Main|List of self-complementary rules}} --->
<!-- {{Main|List of self-complementary rules}} --->
The most well-known and well-investigated self-complementary rule is [[Day & Night]] (B3678/S34678).
The most well-known and well-investigated self-complementary rule is [[Day & Night]] (B3678/S34678).

Revision as of 10:13, 9 July 2017

An (outer-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 outer-totalistic rules.

Examples

The most well-known and well-investigated self-complementary rule is Day & Night (B3678/S34678).