Non-Replicative Fredkin's Rules in Homogeneous Cellular Spaces

In the fifties John von Neumann intensely studied the problem of self-reproduction of configurations in computationally universal cellular automata as a model of biological evolution. Later, Edward Fredkin demonstrated that trivial reproduction is easy to obtain, if we ignore the constraints of universality.

In the present work we extend the boundaries of classical notion of cellular automaton (CA), presenting the new notion of "cellular automaton on a homogeneous directed graph", and we demonstrate that applying the rules found by Fredkin on some special structures of this kind does not lead to their well-known replicative behaviour.
We suggest these phenomena as a cellular automata model of CP-violation.

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