A Full Computation-relevant Topological Dynamics Classification of Elementary Cellular Automata
Cellular Automata and Lattice Gases
2013-02-21 v8
Abstract
Cellular automata are both computational and dynamical systems. We give a complete classification of the dynamic behaviour of elementary cellular automata (ECA) in terms of fundamental dynamic system notions such as sensitivity and chaoticity. The "complex" ECA emerge to be sensitive, but not chaotic and not eventually weakly periodic. Based on this classification, we conjecture that elementary cellular automata capable of carrying out complex computations, such as needed for Turing-universality, are at the "edge of chaos".
Keywords
Cite
@article{arxiv.1107.2080,
title = {A Full Computation-relevant Topological Dynamics Classification of Elementary Cellular Automata},
author = {Martin Schuele and Ruedi Stoop},
journal= {arXiv preprint arXiv:1107.2080},
year = {2013}
}