Three-dimensional Fredkin-rule Cellular Automata

This paper concentrates on the self-reproduction property of the Fredkin-rule cellular automata in two dimensions and three dimensions. For researching the two-dimensional Fredkin-rule cellular automata ,we use two-dimensional Moore neighborhood. So we have This the basic Fredkin's rule. In this paper, we will expand this rule. (1) Make this rule easy. Using the Λ3 or Λ4 in (1 0) and (1 1) to replace the Λin ( 4) and ( 5). Using computer simulations for these expanded rules. The result of the simulations is that cellular automata who use the former expanded rules all have the self-reproduction property .In addition, some special rules have the especially phenomena, such as copying-replicate, diffusing-replicate, stripe-replicate and so on. For researching the three-dimensional Fredkin-rule cellular automata, we define the three-dimensional Von Neumann neighborhood in the first. Then we create enough large three-dimension space, and use a cube, a tetrahedron and a spiral line as the initial pattern. Similarly, the result of computer simulations indicates that a three-dimensional Fredkin-rule cellular automata also has the self-reproduction property. The initial pattern of cellular automata who are...