A computation universal two dimensional state triangular reversible cellular automaton

A reversible cellular automaton RCA is a cellular automaton CA whose global func tion is injective and every con guration has at most one predecessor Margolus showed that there is a computation universal two dimensional state RCA But his RCA has non uniform neighbor so Morita and Ueno proposed state computation universal RCA using partitioned cellular automata PCA Because PCA can be regarded as a subclass of stan dard CA their models has standard neighbor In this paper we show that the number of states of Morita and Ueno s models can be reducible To decrease the number of states from their models with preserving isotropic and bit preserving properties we used triangular neighbor and thus state RCA can be possible This is the smallest state two dimensional RCA under the condition of isotropic property on the framework of PCA We show that our model can simulate basic circuit elements such as unit wires delay elements crossing wires switch gates and inverse switch gates And it is possible to construct a Fredkin gate by combining these elements Since Fredkin gate is known to be a universal logic gate our model has computation universality