Operating binary strings using gliders and eaters in reaction-diffusion cellular automaton
📝 Abstract
We study transformations of 2-, 4- and 6-bit numbers in interactions between traveling and stationary localizations in the Spiral Rule reaction-diffusion cellular automaton. The Spiral Rule automaton is a hexagonal ternary-state two-dimensional cellular automaton – a finite-state machine imitation of an activator-inhibitor reaction-diffusion system. The activator is self-inhibited in certain concentrations. The inhibitor dissociates in the absence of the activator. The Spiral Rule cellular automaton has rich spatio-temporal dynamics of traveling (glider) and stationary (eater) patterns. When a glider brushes an eater the eater may slightly change its configuration, which is updated once more every next hit. We encode binary strings in the states of eaters and sequences of gliders. We study what types of binary compositions of binary strings are implementable by sequences of gliders brushing an eater. The models developed will be used in future laboratory designs of reaction-diffusion chemical computers.
💡 Analysis
We study transformations of 2-, 4- and 6-bit numbers in interactions between traveling and stationary localizations in the Spiral Rule reaction-diffusion cellular automaton. The Spiral Rule automaton is a hexagonal ternary-state two-dimensional cellular automaton – a finite-state machine imitation of an activator-inhibitor reaction-diffusion system. The activator is self-inhibited in certain concentrations. The inhibitor dissociates in the absence of the activator. The Spiral Rule cellular automaton has rich spatio-temporal dynamics of traveling (glider) and stationary (eater) patterns. When a glider brushes an eater the eater may slightly change its configuration, which is updated once more every next hit. We encode binary strings in the states of eaters and sequences of gliders. We study what types of binary compositions of binary strings are implementable by sequences of gliders brushing an eater. The models developed will be used in future laboratory designs of reaction-diffusion chemical computers.
📄 Content
Operating binary strings using gliders and eaters in reaction-diffusion cellular automaton Andrew Adamatzky∗, Genaro Martinez, Liang Zhang, Andrew Wuensche† October 25, 2018 Center for Unconventional Computing and Department of Computer Science University of the West of England, Bristol, United Kingdom Abstract We study transformations of 2-, 4- and 6-bit numbers in interactions between traveling and stationary localizations in the Spiral Rule reaction- diffusion cellular automaton. The Spiral Rule automaton is a hexagonal ternary-state two-dimensional cellular automaton – a finite-state machine imitation of an activator-inhibitor reaction-diffusion system. The activa- tor is self-inhibited in certain concentrations. The inhibitor dissociates in the absence of the activator. The Spiral Rule cellular automaton has rich spatio-temporal dynamics of traveling (glider) and stationary (eater) patterns. When a glider brushes an eater the eater may slightly change its configuration, which is updated once more every next hit. We encode binary strings in the states of eaters and sequences of gliders. We study what types of binary compositions of binary strings are implementable by sequences of gliders brushing an eater. The models developed will be used in future laboratory designs of reaction-diffusion chemical computers. Keywords: cellular automata, reaction-diffusion computing, gliders, collision- based computing 1 Introduction Many physical, chemical and biological spatially extended non-linear systems exhibit a wide range of stationary and mobile localizations: solitons, kinks, breathers, excitons, defects and wave-fragments. The localizations can be used to transmit and transform information, and ultimately to perform computa- tion [1]. A unit of information, such as the value of a Boolean variable, is decoded into presence (logical truth) or absence (logical false) of a localiza- tion in some specified site of space at a specified moment of time. When two localizations (representing the values of two logical variables) collide, they change their trajectories (or annihilate, reproduce, or change their shape). The ∗Contact author: andrew.adamatzky@uwe.ac.uk †www.ddlab.org 1 arXiv:0908.0853v1 [cs.FL] 6 Aug 2009 new trajectories of the localizations encode the values of some logical function over the two variables. This is how most collision-based computing devices work [7, 10, 13, 1, 8, 19, 20, 14]. The collision-based, or free-space, computing devices typically do not have wires and — in principle – are not supposed to use any other stationary com- ponents to perform computation. Any point of the computing media can act as a wire, a trajectory of a traveling localization can be seen as a momentary wire. Any site where two or more localizations collide is a logical gate. Thus space can be used efficiently and nothing is wasted. However, there is a price to pay. Initial positions and launch time of the traveling localizations should be precisely specified: one wrong time step destroys the whole computing scheme. The need for perfect timing is the weakest point of collision-based computing and the subject of constant criticism by “classical” computation schools. Can we do without perfect timing? Asynchronous cellular-automaton based computers do pretty well [11, 15, 12] by using predetermined wires and valves. In the present paper we are trying to combine pure collision-based computing ideas (gliders only) with stationary architectures (breather-like localization) to implement computing schemes with relaxed timing. We choose the reaction- diffusion Sprial Rule cellular automaton [18, 4, 3, 16] as a testbed for ideas of asynchronous collision-based computing. What is our rationale behind selecting the Spiral Rule automaton to study novel concepts of the collision-based computing? The Spiral Rule cellular au- tomaton [18] plays a unique role in unconventional computing. On the one hand, this is a simple ternary state hexagonal automaton with Conway’s Game of Life type of behavior: it has gliders, still lives and eaters, and glider. Therefore it is very suitable for experimenting with collision-based computing schemes. On the other hand, the Spiral Rule automaton is a unique discrete model of a non-linear reaction-diffusion chemical system with an activator and inhibitor. The gliders and glider guns in the Spiral Rule automaton are analogues of excitation wave- fragments and generators of wave-fragments in a light-sensitive sub-excitable Belousov-Zhabotinsky medium [9]. This means that prototypes of computing schemes designed in the Spiral Rule automaton can then be almost straight- forwardly implemented in chemical laboratory prototypes of reaction-diffusion computers. The paper is structured as follows. The Spiral Rule reaction-diffusion cellular automaton is defined in Sect. 2. Encoding of two- and four-bit binary strings in states of an eater and transformation of the strings by gliders are presented in Sect. 3. Section 4 studie
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