Excitable Delaunay triangulations

In an excitable Delaunay triangulation every node takes three states (resting, excited and refractory) and updates its state in discrete time depending on a ratio of excited neighbours. All nodes update their states in parallel. By varying excitability of nodes we produce a range of phenomena, including reflection of excitation wave from edge of triangulation, backfire of excitation, branching clusters of excitation and localized excitation domains. Our findings contribute to studies of propagating perturbations and waves in non-crystalline substrates

On polymorphic logical gates in sub-excitable chemical medium

In a sub-excitable light-sensitive Belousov-Zhabotinsky chemical medium an asymmetric disturbance causes the formation of localized traveling wave-fragments. Under the right conditions these wave-fragment can conserve their shape and velocity vectors for extended time periods. The size and life span of a fragment depend on the illumination level of the medium. When two or more wave-fragments collide they annihilate or merge into a new wave-fragment. In computer simulations based on the Oregonator model we demonstrate that the outcomes of inter-fragment collisions can be controlled by varying the illumination level applied to the medium. We interpret these wave-fragments as values of Boolean variables and design collision-based polymorphic logical gates. The gate implements operation XNOR for low illumination, and it acts as NOR gate for high illumination. As a NOR gate is a universal gate then we are able to demonstrate that a simulated light sensitive BZ medium exhibits computational universality

Towards constructing one-bit binary adder in excitable chemical medium

Light-sensitive modification (ruthenium catalysed) of the Belousov-Zhabotinsky medium exhibits various regimes of excitability depending on the levels of illumination. For certain values of illumination the medium switches to a sub-excitable mode. An asymmetric perturbation of the medium leads to formation of a travelling localized excitation, a wave-fragment which moves along a predetermined trajectory, ideally preserving its shape and velocity. To implement collision-based computing with such wave-fragments we represent values of Boolean variables in presence/absence of a wave-fragment at specific sites of medium. When two wave-fragments collide they either annihilate, or form new wave-fragments. The trajectories of the wave-fragments after the collision represent a result of the computation, e.g. a simple logical gate. Wave-fragments in the sub-excitable medium are famously difficult to control. Therefore, we adopted a hybrid procedure in order to construct collision-based logical gates: we used channels, defined by lower levels illumination to subtly tune the shape of a propagating wave-fragment and allow the wave-fragments 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 arithmetical circuits in spatially-extended excitable chemical systems