Fredkin and Toffoli gates implemented in Oregonator model of Belousov-Zhabotinsky medium

Abstract: A thin-layer Belousov-Zhabotinsky (BZ) medium is a powerful computing device capable for implementing logical circuits, memory, image processors, robot controllers, and neuromorphic architectures. We design the reversible logical gates --- Fredkin gate and Toffoli gate --- in a BZ medium network of excitable channels with sub-excitable junctions. Local control of the BZ medium excitability is an important feature of the gates' design. A excitable thin-layer BZ medium responds to a localised perturbation with omnidirectional target or spiral excitation waves. A sub-excitable BZ medium responds to an asymmetric perturbation by producing travelling localised excitation wave-fragments similar to dissipative solitons. We employ interactions between excitation wave-fragments to perform computation. We interpret the wave-fragments as values of Boolean variables. A presence of a wave-fragment at a given site of a circuit represents logical truth, absence of the wave-fragment --- logical false. Fredkin gate consists of ten excitable channels intersecting at eleven junctions eight of which are sub-excitable. Toffoli gate consists of six excitable channels intersecting at six junctions four of which are sub-excitable. The designs of the gates are verified using numerical integration of two-variable Oregonator equations.