Dynamic State Networks

Alec Resnick and Jesse Louis-Rosenberg

Massachusetts Institute of Technology

Dynamic state network (DSN), a graph whose nodes contain states and edges that represent lines of influence between nodes. Rules that act over edges can be defined on these networks to create a system of dynamic states.

Recasting cellular automata in the language of the DSN, conventional measures of entropy are shown to generalize poorly to arbitrary networks. Novel measures of network entropy that address this challenge are introduced. These measures are used to reinterpret the nature of traditional cellular automata, implemented with the machinery of the DSN.

Traditionally, the concept of entropy has been central to the analysis of cellular automata behavior. However, entropic considerations have provided an inadequate theoretical framework for understanding the basic nature of cellular automata. This motivates the introduction of the DSN, built upon the foundation of network theory. The accompanying theoretical environment is less ambiguous, allowing for a more powerfully abstracted treatment of the subject.

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