Elementary Nearest Ambidextrous Automata

Elementary rules return one output bit for three input bits. It is thus possible to apply such rules to any context that expects one output bit for three binary inputs. This kind of generalization is illustrated by a system which evolves arbitrary real positions by inverting a binary state value for each position according to its previous state bit and those of its two nearest neighbors.

At each step the elementary rule updates the states of all binary particles. The updated state value decides whether the mean of those three positions is added to the previous position of the processed particle after a rotation of the mean position by either 90 or -90 degrees.