Towards constructing one-bit binary adder in excitable chemical medium

Abstract

The light-sensitive modification (ruthenium catalysed) of the Belousov–Zhabotinsky reaction exhibits various excitability regimes depending on the level of illumination. Within a narrow range of applied illumination levels the medium is in a sub-excitable state. When in this state an asymmetric perturbation of the medium leads to formation of a travelling localized excitation (wave-fragment) which moves along a predetermined trajectory, ideally preserving its shape and velocity over an extended time period. Collision-based computing can be implemented with these wave-fragments whereby values of Boolean variables are represented as the presence/absence of a wave-fragment at specific sites. When two wave-fragments collide they either annihilate, or form new wave-fragments. The trajectories of the wave-fragments after the collision represent the result of a computation, e.g. construction of a simple logical gate. However, wave-fragments in sub-excitable chemical media are difficult to control. Therefore, we adopted a hybrid procedure in order to construct collision-based logical gates. We used channels of low light intensity projected onto the excitable media in order to subtly tune and stabilise the propagating wave-fragments allowing them to collide at the junctions between channels. Using this methodology we were able to implement both in theoretical models (using the Oregonator) and in experiment two interaction-based logical gates and assemble the gates into a basic one-bit binary adder. We present the first ever experimental approach towards constructing arithmetic circuits in spatially-extended excitable chemical systems where light is used to impart functionality.