Subexcitable Belousov-Zhabotinsky Research Articles

Computational modalities of Belousov–Zhabotinsky encapsulated vesicles

We present both simulated and partial empirical evidences for the computational utility of many connected vesicle analogues of an encapsulated nonlinear chemical processing medium. By connecting small vesicles containing a solution of sub-excitable Belousov–Zhabotinsky (BZ) reaction, sustained and propagating wave fragments are modulated by both spatial geometry, network connectivity and their interaction with other waves. The processing ability is demonstrated through the creation of simple Boolean logic gates and then by the combination of those gates to create more complex circuits.

If BZ medium did spanning trees these would be the same trees as Physarum built

A sub-excitable Belousov–Zhabotinsky (BZ) medium exhibits self-localized wave-fragments which may travel for relatively long time preserving their shape. Using Oregonator model of the BZ medium we imitate foraging behavior of a true slime mold, Physarum polycephalum, on a nutrient-poor substrate. We show that given erosion post-processing operations the BZ medium can approximate a spanning tree of a planar set and thus is computationally equivalent to Physarum in the domain of proximity graph construction.

Dynamic control and information processing in the Belousov–Zhabotinsky reaction using a coevolutionary algorithm

We propose that the behavior of nonlinear media can be controlled dynamically through coevolutionary systems. In this study, a light-sensitive subexcitable Belousov-Zhabotinsky reaction is controlled using a heterogeneous cellular automaton. A checkerboard image comprising of varying light intensity cells is projected onto the surface of a catalyst-loaded gel resulting in rich spatiotemporal chemical wave behavior. The coevolved cellular automaton is shown to be able to either increase or decrease chemical activity through dynamic control of the light intensity within each cell in both simulated and real chemical systems. The approach is then extended to construct a number of simple logical functions.

Experimental validation of binary collisions between wave fragments in the photosensitive Belousov–Zhabotinsky reaction

We present experimental verification of wave fragment collisions in the sub-excitable Belousov–Zhabotinsky medium observed previously in simulation [Adamatzky A, De Lacy Costello B. Binary collisions between wave fragments in a sub-excitable Belousov–Zhabotinsky medium. Chaos, Solitons & Fractals 2007;34:307–15]. We have reproduced in chemical experiments the majority of the collisions observed in simulation including annihilation, fusion and quasi-elastic types. The method we present is capable of implementing information transfer without any rigidly controlled architecture – fragments are simply introduced into an “arena” which consists of a large area of gel illuminated with a uniform light level – controlled at a level close to the sub-excitable threshold. Therefore, the fragments of excitation both pre and post collision possess a considerable freedom of movement when compared to previous implementations of information transfer in chemical systems. This chemical verification of previous theoretical results brings closer the possibility of utilising this phenomenon for implementing collision-based gates, signal tuning and programming of collision-based computers based upon excitable chemical reactions.

Towards Unconventional Computing through Simulated Evolution: Control of Nonlinear Media by a Learning Classifier System

We propose that the behavior of nonlinear media can be controlled automatically through evolutionary learning. By extension, forms of unconventional computing (viz., massively parallel nonlinear computers) can be realized by such an approach. In this initial study a light-sensitive subexcitable Belousov-Zhabotinsky reaction in which a checkerboard image, composed of cells of varying light intensity projected onto the surface of a thin silica gel impregnated with a catalyst and indicator, is controlled using a learning classifier system. Pulses of wave fragments are injected into the checkerboard grid, resulting in rich spatiotemporal behavior, and a learning classifier system is shown to be able to direct the fragments to an arbitrary position through dynamic control of the light intensity within each cell in both simulated and real chemical systems. Similarly, a learning classifier system is shown to be able to control the electrical stimulation of cultured neuronal networks so that they display elementary learning. Results indicate that the learned stimulation protocols identify seemingly fundamental properties of in vitro neuronal networks. Use of another learning scheme presented in the literature confirms that such fundamental behavioral characteristics of a given network must be considered in training experiments.

Binary collisions between wave-fragments in a sub-excitable Belousov–Zhabotinsky medium

In numerical studies we describe the phenomenology of interactions between localized, shape-preserving, wave-fragments in the sub-excitable Belousov–Zhabotinsky medium and build a representative catalog of wave-fragment collisions that include annihilation, fusion, and quasi-elastic types. We envisage the phenomena discovered will be used in signal tuning and general programming of collision-based [Adamatzky A, editor, Collision-based computing. Springer-Verlag, 2002] excitable chemical computers.

Collision-based computing in Belousov–Zhabotinsky medium

A photosensitive sub-excitable Belousov–Zhabotinsky medium exhibits propagating wave fragments that preserve their shapes during substantial periods of time. In numerical studies we show that the medium is a computational universal architectureless system, if presence and absence of wave fragments are interpreted as truth values of Boolean variable. When two or more wave fragments collide they may annihilate, fuse, split or deviate from their original paths, thus values of the logical variables are changed and certain logical gates are realized in result of the collision. We demonstrate exact implementation of basic operations with signals and logical gates in Belousov–Zhabotinsky dynamic circuits. The findings provide a theoretical background for subsequent experimental implementation of collision-based, architectureless, dynamical computing devices in homogeneous active chemical media.