Towards Arithmetic Circuits in Sub‐Excitable Chemical Media

Abstract

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.

Chemical computing with reaction–diffusion processes

“…For low light intensity, it becomes excitable so the system of equations (2.1) and (2.2) should allow for propagation of spikes. A very careful tuning of medium parameters (φ) produces wave fragments that do not shrink or expand while propagating over short distances and their shapes depend on initial perturbations [34]. If the medium is exposed to high intensity of light, then it exhibits no nonlinear behaviour, because for φ >> 0 the system of equations (2.1) and (2.2) has a strongly attractive stable state.…”

“…Complex information processing operations can be performed even for relatively simple reaction kinetics if the geometrical distribution of regions with high or low excitability level is carefully prepared. In a series of recent papers, Adamatzky and co-workers considered the logic gates, as well as some selected arithmetic operations, executed by a system of sub-excitable discs [34,[43][44][45][46]. Their simulation results were supported by experiments with Ru-catalysed BZ reaction in which the catalyst was immobilized on a membrane and the membrane was placed in a solution of the other reagents of BZ reaction [46].…”

Computing in Verotoxin

“…[21] Computingw ith propagating excitation wave-fronts was found to be so efficient that aw ide range of computing devices has been realised, including information frequency coders, [22] chemical diodes, [23] logic gates, [20,24] and arithmeticc ircuits. [25][26][27][28][29] Macro-designso fc omputing schemes based on interaction of excitation waves-frontso rt ravelling localised excitations have as ubstantial drawback:t hey are very slow when implemented in chemical systems.…”

On Half-Adders Based on Fusion of Signal Carriers: Excitation, Fluidics, and Electricity

“…Time lapse snapshots provided in the paper were recorded at every 150 time steps, we display sites with u > 0.04. The model has been repeatedly verified by us in experimental laboratory studies of BZ system, and the satisfactory match between the model and the experiments has been demonstrated in [6,17,39,5]. Geometry of the fusion gate F is shown in Fig.…”