Causal dynamics of discrete manifolds

2018/05/25 by Pablo Arrighi, Arrighi, Pablo, Clément Chouteau +5
Computer Science · Mathematics · #Cellular Automata and Applications #Combinatorics (math.CO) #Computational Geometry (cs.CG) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1805.10051

openalex publication_date 2018/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend Cellular Automata to time-varying discrete geometries. In other words we formalize, and prove theorems about, the intuitive idea of a discrete manifold which evolves in time, subject to two natural constraints: the evolution does not propagate information too fast; and it acts everywhere the same. For this purpose we develop a correspondence between complexes and labeled graphs. In particular we reformulate the properties that characterize discrete manifolds amongst complexes, solely in terms of graphs. In dimensions n<4, over bounded-star graphs, it is decidable whether a Cellular Automaton maps discrete manifolds into discrete manifolds.

Related

• Causal graph dynamics
• Universality of causal graph dynamics
• Discrete Mathematics and Physics on the Planck-Scale exemplified by means of a Class of 'Cellular Network Models' and their Dynamics
• Discrete mechanics: a sequential growth dynamics for causal sets, and a self-organization of particles
• From the discrete to the continuous, from simplicial complexes to Riemannian manifolds. Approximating flows and cuts on manifolds by discrete versions