Hopeful windows and fractals in cellular automata and combinatorial games
Combinatorics
2016-06-07 v1 Dynamical Systems
Abstract
This paper studies 2-player impartial combinatorial games, where the outcomes correspond to updates of cellular automata (CA) which generalize Wolfram's elementary rule 60 and rule 110 (Cook 2004). The games extend the class of \emph{triangle placing games} (Larsson 2013) where at each stage of the game the previous player has the option to block certain hopeful moves of the next player. We also study fractals and partial convergence in a subclass of the CA.
Keywords
Cite
@article{arxiv.1606.01758,
title = {Hopeful windows and fractals in cellular automata and combinatorial games},
author = {Urban Larsson},
journal= {arXiv preprint arXiv:1606.01758},
year = {2016}
}
Comments
11 pages, 10 figures