The Strange Man in Random Networks of Automata

TL;DR

This study uses computer simulations to analyze damage propagation and phase transitions in automata on various graph structures, revealing that damage speed is sensitive to network topology and dilution, but the transition to chaos remains unaffected by a damaging agent.

Contribution

It introduces the concept of a 'strange man' damaging agent and investigates its effects on damage spreading and phase transitions across different network types.

Findings

Damage propagation speed follows a power law with a lattice-dependent exponent.

Adding the damaging agent does not alter the transition to chaos.

Damage speed is highly sensitive to network dilution and structure.

Abstract

We have performed computer simulations of Kauffman's automata on several graphs such as the regular square lattice and invasion percolation clusters in order to investigate phase transitions, radial distributions of the mean total damage (dynamical exponent $z$) and propagation speeds of the damage when one adds a damaging agent, nicknamed "strange man". Despite the increase in the damaging efficiency, we have not observed any appreciable change at the transition threshold to chaos neither for the short-range nor for the small-world case on the square lattices when the strange man is added in comparison to when small initial damages are inserted in the system. The propagation speed of the damage cloud until touching the border of the system in both cases obeys a power law with a critical exponent $\alpha$ that strongly depends on the lattice. Particularly, we have ckecked the damage spreading when some connections are removed on the square lattice and when one considers special invasion percolation clusters (high boundary-saturation clusters). It is seen that the propagation speed in these systems is quite sensible to the degree of dilution.