Cellular Automata on Graphs: Topological Properties of ER Graphs Evolved towards Low-Entropy Dynamics

Entropy

Carsten Marr¹ 

[1] Institute for Bioinformatics and Systems Biology, Helmholtz Zentrum München, German Research Center for Environmental Health, D-85764 Neuherberg, Germany; E-Mail:

关键词: network dynamics;    simulated evolution;    cellular automata on graphs;    dynamic probes;   

DOI  :  10.3390/e14060993

来源: mdpi

【 摘 要 】

Cellular automata (CA) are a remarkably efficient tool for exploring general properties of complex systems and spatiotemporal patterns arising from local rules. Totalistic cellular automata, where the update rules depend only on the density of neighboring states, are at the same time a versatile tool for exploring dynamical processes on graphs. Here we briefly review our previous results on cellular automata on graphs, emphasizing some systematic relationships between network architecture and dynamics identified in this way. We then extend the investigation towards graphs obtained in a simulated-evolution procedure, starting from Erdős–Rényi (ER) graphs and selecting for low entropies of the CA dynamics. Our key result is a strong association of low Shannon entropies with a broadening of the graph’s degree distribution.

【 授权许可】

CC BY   
© 2012 by the authors; licensee MDPI, Basel, Switzerland.