Max-Plus Generalization of Conway's Game of Life
Kotaro Sakata, Yuta Tanaka, Daisuke Takahashi
TL;DR
This paper introduces a max-plus equation that generalizes Conway's Game of Life, unifying various solutions and extending it to multi-value scenarios, with discussions on solution behaviors.
Contribution
It presents a novel max-plus framework that encompasses and extends Conway's Game of Life, including multi-value solutions.
Findings
Max-plus equation includes GoL as a special case
Special solutions unify various GoL variants
Multi-value extension derived and analyzed
Abstract
We propose a max-plus equation which includes Conway's Game of Life (GoL) as a special case. There are some special solutions to the equation which include and unify those to GoL. Moreover, the multi-value extension of GoL is derived from the equation and the behavior of solutions is discussed.
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Taxonomy
TopicsAlgorithms and Data Compression · Logic, programming, and type systems · semigroups and automata theory