A universal non-conservative reversible elementary triangular partitioned cellular automaton that shows complex behavior

We study a simple triangular partitioned cellular automaton (TPCA), and clarify its complex behavior. It is a CA with triangular cells, each of which is divided into three parts. The next state of a cell is determined by the three adjacent parts of its neighbor cells. This framework makes it easy to...

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Bibliographic Details
Published in:Natural computing 2019-09, Vol.18 (3), p.413-428
Main Author: Morita, Kenichi
Format: Article
Language:English
Subjects:
Artificial Intelligence
Cellular automata
Complex Systems
Computer Science
Evolutionary Biology
Gliders
Logic circuits
Processor Architectures
Theory of Computation
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Summary:We study a simple triangular partitioned cellular automaton (TPCA), and clarify its complex behavior. It is a CA with triangular cells, each of which is divided into three parts. The next state of a cell is determined by the three adjacent parts of its neighbor cells. This framework makes it easy to design reversible triangular CAs. Among them, isotropic and eight-state (i.e., each part has only two states) TPCAs are called elementary TPCAs (ETPCAs). They are extremely simple, since each of their local transition functions is described by only four local rules. In this paper, we investigate a specific reversible ETPCA T 0347 , where 0347 is its identification number in the class of 256 ETPCAs. In spite of the simplicity of the local function and the constraint of reversibility, evolutions of configurations in T 0347 have very rich varieties. It is shown that a glider, which is a space-moving pattern, and glider guns exist in this cellular space We also show that the trajectory and the timing of a glider can be fully controlled by appropriately placing stable patterns called blocks. Furthermore, using gliders to represent signals, we can implement universal reversible logic gates in it. By this, computational universality of T 0347 is derived.
ISSN:1567-7818
1572-9796
DOI:10.1007/s11047-017-9655-9