A maze routing algorithm based on two dimensional cellular automata

This paper propose a maze routing algorithm based on cellular automata. The aim of this algorithm is find the shortest path between the source cell and the target cell, so that the path does not pass from the obstacles. Algorithm has two phases, exploration and retrace. In exploration phase a wave is expanded from source cell and it puts token on cells which it passes via them while expanding. In the retracing phase, we start from target cell, follow the wave and arrive to source cell; the path created in this phase is desirable. Propose algorithm is simple and it's transactions are local and follow the cellular automata properties. This algorithm find the desirable path in m x m two dimensional CA in O(m(2)) time step.