Computation of shortest path in cellular automata

In this paper, we show how to find the shortest path between given nodes of a mesh with weighted edges. We use a cellular automaton which exhibits autowave patterns, where a wave of auto-excitation originates in source node, spreads around the mesh, and modifies states of the cells to make a stationary pattern isomorphed to the shortest path from source node to destination one. For different formulations of the shortest path problem, and various cellular automata (which solve it), we proved the bounds of complexity. For the sake of clarity, we present several examples of cellular automata computation of the shortest path. They are illustrated in detail.