Julian Holley

Computational modalities of Belousov–Zhabotinsky encapsulated vesicles

Abstract 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.

On architectures of circuits implemented in simulated Belousov–Zhabotinsky droplets

When lipid vesicles filled with Belousov-Zhabotinsky (BZ) excitable chemical medium are packed in tight assembles, waves of excitation may travel between the vesicles. When several waves meet in a vesicle some fragments may deflect, others can annihilate or continue their travel undisturbed. By interpreting waves as Boolean values we can construct logical gates and assemble them in large circuits. In numerical modelling we show two architectures of one-bit half-adders implemented in BZ-vesicles.

Vesicle computers: Approximating a Voronoi diagram using Voronoi automata

Abstract Irregular arrangements of vesicles filled with excitable and precipitating chemical systems are imitated by Voronoi automata – finite-state machines defined on a planar Voronoi diagram. Every Voronoi cell takes four states: resting, excited, refractory and precipitate. A resting cell excites if it has at least one neighbour in an excited state. The cell precipitates if the ratio of excited cells in its neighbourhood versus the number of neighbours exceeds a certain threshold. To approximate a Voronoi diagram on Voronoi automata we project a planar set onto the automaton lattice, thus cells corresponding to data-points are excited. Excitation waves propagate across the Voronoi automaton, interact with each other and form precipitate at the points of interaction. The configuration of the precipitate represents the edges of an approximated Voronoi diagram. We discover the relationship between the quality of the Voronoi diagram approximation and the precipitation threshold, and demonstrate the feasibility of our model in approximating Voronoi diagrams of arbitrary-shaped objects and in constructing a skeleton of a planar shape.

Toward Turing’s A-Type Unorganised Machines in an Unconventional Substrate: A Dynamic Representation in Compartmentalised Excitable Chemical Media

Turing presented a general representation scheme by which to achieve artificial intelligence – unorganised machines. Significantly, these were a form of discrete dynamical system and yet such representations remain relatively unexplored. Further, at the same time as also suggesting that natural evolution may provide inspiration for search mechanisms to design machines, he noted that mechanisms inspired by the social aspects of learning may prove useful. This paper presents initial results from consideration of using Turing’s dynamical representation within an unconventional substrate - networks of Belousov-Zhabotinsky vesicles - designed by an imitation-based, i.e., cultural, approach. Turing’s representation scheme is also extended to include a fuller set of Boolean functions at the nodes of the recurrent networks.