Towards Arithmetical Chips in Sub-Excitable Media: Cellular Automaton Models

Towards Arithmetical Chips in Sub-Excitable Media: Cellular Automaton Models

Liang Zhang (University of the West of England, UK) and Andrew Adamatzky (University of the West of England, UK)
DOI: 10.4018/978-1-60960-186-7.ch015
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Abstract

We discuss a theoretical design of an arithmetical chip built on an excitable medium substrate. The chip is simulated in a two-dimensional three-state cellular automaton with eight-cell neighborhoods. Every resting cell is excited if it has exactly two excited neighbors, the excited cells takes refractory state unconditionally. A transition from refractory back to resting state also happens irrelevantly to a state of the cell neighborhood. The design is based on principles of collision-based computing. Boolean logic values are encoded by traveling localizations, or particles. Logical gates are realized in collisions between the particles. Detailed blue prints of collision-based adders and multipliers presented in the article pave the way to future laboratory experimental prototypes of general-purpose chemical computers.
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Cellular-Automaton Model Of Sub-Excitable Media

We employ a two-dimensional three-state cellular-automaton model of an excitable medium — the 2+-medium, originally introduced in (Adamatzky, 1995; Adamatzky, 1998). The 2+-medium consists of an orthogonal array of finite automata, where every automaton, called a cell, takes three states: resting, excited ‘+’ and refractory ‘-‘ and updates its state depending on the states of its eight neighbors. All cells update their states simultaneously and in discrete time, using the same rule. A resting cell becomes excited if it has exactly two excited neighbors. The transitions from excited state to refractory state, and from refractory state to resting state are unconditional.

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