Damaging 2D Quantum Gravity

TL;DR

This paper explores how damage spreads in a cellular automaton coupled with 2D quantum gravity, revealing insights into complex interactions between automaton dynamics and fluctuating graph geometries.

Contribution

It introduces a numerical study of damage spreading on a dynamical $\, ext{phi}^3$ graph, bridging fixed and annealed automaton models in the context of 2D gravity.

Findings

Damage spreading behavior is influenced by the dynamical graph structure.

The model provides a new perspective on automaton behavior coupled with quantum gravity.

Results suggest complex interplay between automaton rules and graph geometry.

Abstract

We investigate numerically the behaviour of damage spreading in a Kauffman cellular automaton with quenched rules on a dynamical $\phi^3$ graph, which is equivalent to coupling the model to discretized 2D gravity. The model is interesting from the cellular automaton point of view as it lies midway between a fully quenched automaton with fixed rules and fixed connectivity and a (soluble) fully annealed automaton with varying rules and varying connectivity. In addition, we simulate the automaton on a fixed $\phi^3$ graph coming from a 2D gravity simulation as a means of exploring the graph geometry.