Synthesis of Scalable Single Length Cycle, Single Attractor Cellular Automata in Linear Time
- 15 September 2021
- journal article
- research article
- Published by Wolfram Research, Inc. in Complex Systems
- Vol. 30 (3), 415-439
- https://doi.org/10.25088/complexsystems.30.3.415
Abstract
This paper proposes the synthesis of single length cycle, single attractor cellular automata (SACAs) for arbitrary length. The n-cell single length cycle, single attractor cellular automaton (SACA), synthesized in linear time O(n), generates a pattern and finally settles to a point state called the single length cycle attractor state. An analytical framework is developed around the graph-based tool referred to as the next state transition diagram to explore the properties of SACA rules for three-neighborhood, one-dimensional cellular automata. This enables synthesis of an (n + 1)-cell SACA from the available configuration of an n-cell SACA in constant time and an (n + m)-cell SACA from the available configuration of n-cell and m-cell SACAs also in constant time.Keywords
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