Signals for Cellular Automata in dimension 2 or higher
Jean-Christophe Dubacq (LIPN, GREYC), Veronique Terrier (GREYC)
TL;DR
This paper explores how increasing the dimension of cellular automata arrays facilitates the construction of signals, reducing the number of states needed and revealing a gap in constructible signals across dimensions.
Contribution
It demonstrates the existence of a signal gap in any dimension and provides two 2D cellular automata examples showing dimension increase reduces state complexity.
Findings
Existence of a constructible signal gap in all dimensions
Increasing dimension reduces the number of states needed for certain signals
Two 2D cellular automata examples illustrate these benefits
Abstract
We investigate how increasing the dimension of the array can help to draw signals on cellular automata.We show the existence of a gap of constructible signals in any dimension. We exhibit two cellular automata in dimension 2 to show that increasing the dimension allows to reduce the number of states required for some constructions.
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Taxonomy
TopicsCellular Automata and Applications