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Network Analysis of the State Space of Discrete Dynamical Systems

Amer Shreim·Peter Grassberger·Walter Nadler·Björn Samuelsson·Joshua E. S. Socolar·Maya Paczuski
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Abstract

We study networks representing the dynamics of elementary 1-d cellular automata (CA) on finite lattices. We analyze scaling behaviors of both local and global network properties as a function of system size. The scaling of the largest node in-degree is obtained analytically for a variety of CA including rules 22, 54 and 110. We further define the \emph{path diversity} as a global network measure. The co-appearance of non-trivial scaling in both hub size and path diversity separates simple dynamics from the more complex behaviors typically found in Wolfram's Class IV and some Class III CA.

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BibTeXRIS

Amer Shreim, Peter Grassberger, Walter Nadler, Björn Samuelsson, Joshua E. S. Socolar, Maya Paczuski. 2007-03-06. Network Analysis of the State Space of Discrete Dynamical Systems. https://doi.org/10.1103/physrevlett.98.198701

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