OCA:Day & Night
Day and Night is a fanciful variant of Conway's Life which has at least two inspirations from popular culture. The Life universe, a two dimensional square grid whose binary cells are referred to as 'live' or 'dead' (or 'unoccuied'), or even zeroes and ones, quickly evolves from random initial conditions into a sparsely populated state. Binary automata are associated with complementary automata wherein zeroes and ones are interchanged; some are symmetric with respect to this exchange. Watching Life evolving quickly reminded observers of two similar situations:
- A well known engraving by Maurits Escher actually entitled Day and Night featured a flock of black birds flying against a background of similarly flying white birds - mirror images of each other.
- The symmetry between electrons and the eventually discovered positrons in P. A. M. Dirac's relativistic quantum mechanics.
It was therefore a temptation to adjust the rules of Life to invoke such a symmetry. The 180 degree rotational symmetry of the return map of such a rule places an unstable fixed point at density 1/2, resulting in a characteristic dynamics at boundaries where day meets night. Normal Life evolution or its complement is expected to occur elsewhere.