Phys. Rev. Lett. 98, 198701 (2007) [4 pages]Network Analysis of the State Space of Discrete Dynamical SystemsReceived 20 October 2006; published 8 May 2007 We study networks representing the dynamics of elementary 1D 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 path diversity as a global network measure. The coappearance of nontrivial scaling in both the hub size and the path diversity separates simple dynamics from the more complex behaviors typically found in Wolfram’s class IV and some class III CA. © 2007 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.98.198701
DOI:
10.1103/PhysRevLett.98.198701
PACS:
89.75.Hc, 89.75.Da, 89.75.Fb
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