Path Rewriting Cellular Automata

Path rewriting cellular automata evolve in the following fashion: every system operates on a network where each node has one state and one outgoing connection. At each step, each node looks at it's own state and the states of the nodes following successive connections ahead of it. The node then uses these states to decide two things: the new state of the node, and which 'downstream' node it will be connected to on the following step. The rule icon here shows what a node will do with a particular sequence. The leftmost cell is the node itself, and there are two 'downstream' connections. A cell in the top center means that the node stays connected to the one it was already connected to, while a top right cell means that the node jumps ahead to the one following the one it was connected to.