A Life-Like Rule Where Random Islands Either Grow or Shrink

The life-like cellular Automata rule B34678/S3678 is a state symmetric rule with the unusual property that any area of one state in a universe of the other will transform into an area which is a chaotic mixture of both states. This area may either expand to fill the universe or shrink to an empty universe or a few small stable patterns. Larger patterns are more likely to expand than small ones. Statistical analysis of this behaviour is presented. It is noted that the chaotic mixture behaves like an extra state which is not symmetric with the others representing emergence of asymmetry.