Fixed Point Constructions in Tilings and Cellular Automata
Dynamical Systems
2021-05-04 v1 Computational Complexity
Logic
Abstract
The fixed point construction is a method for designing tile sets and cellular automata with highly nontrivial dynamical and computational properties. It produces an infinite hierarchy of systems where each layer simulates the next one. The simulations are implemented entirely by computations of Turing machines embedded in the tilings or spacetime diagrams. We present an overview of the construction and list its applications in the literature.
Keywords
Cite
@article{arxiv.2105.00443,
title = {Fixed Point Constructions in Tilings and Cellular Automata},
author = {Ilkka Törmä},
journal= {arXiv preprint arXiv:2105.00443},
year = {2021}
}
Comments
15 pages. To be presented at AUTOMATA 2021 as an invited talk