A causal graph (or causal network) is an acyclic digraph arising from an evolution of a substitution system (Wolfram 2002, pp. 486--524) or other update system (Wolfram). The nodes of a causal graph represent updating events and its edges represent their causal relationships (Wolfram). The graph itself therefore represent the history of the system. The illustration above shows a causal network corresponding to the rules {B B->A, A A B->B A A B} (applied in a left-to-right scan) and initial condition A B A A B (Wolfram 2002, p. 498, fig. a). The figure above shows the procedure for diagrammatically creating a causal graph from a mobile automaton.
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