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Cellular Automata on Graphs: Topological Properties of ER Graphs Evolved towards Low-Entropy Dynamics
Institute for Bioinformatics and Systems Biology, Helmholtz Zentrum München, German Research Center for Environmental Health, D-85764 Neuherberg, Germany
Computational Systems Biology, School of Engineering and Science, Jacobs University Bremen, D-28759 Bremen, Germany
* Author to whom correspondence should be addressed.
Received: 30 April 2012; in revised form: 31 May 2012 / Accepted: 31 May 2012 / Published: 5 June 2012
Abstract: 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 Erdő s–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.
Keywords: network dynamics; simulated evolution; cellular automata on graphs; dynamic probes
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Cite This Article
MDPI and ACS Style
Marr, C.; Hütt, M.-T. Cellular Automata on Graphs: Topological Properties of ER Graphs Evolved towards Low-Entropy Dynamics. Entropy 2012, 14, 993-1010.
Marr C, Hütt M-T. Cellular Automata on Graphs: Topological Properties of ER Graphs Evolved towards Low-Entropy Dynamics. Entropy. 2012; 14(6):993-1010.
Marr, Carsten; Hütt, Marc-Thorsten. 2012. "Cellular Automata on Graphs: Topological Properties of ER Graphs Evolved towards Low-Entropy Dynamics." Entropy 14, no. 6: 993-1010.