Towards Arithmetic Circuits in Sub-Excitable Chemical Media

A sub-excitable Belousov-Zhabotinsky medium exhibits localized travelling excitations (in contrast to an excitable medium exhibiting target or spiral waves). Initially assymetric perturbations give birth to excitation wave-fragments. The shape and velocity vectors of the wave-fragments are conserved, meaning they can travel for substantial distances in the reaction media. When the wave-fragments collide they may reflect, merge, or annihilate. We interpret wave-fragments as values of logical variables, and the post-collision states of the fragments as outputs of logical gates. We show how to cascade logical gates in primitive arithmetical circuits.