Causal Network


A causal network is an acyclic digraph arising from an evolution of a substitution system, and representing its history. The illustration above shows a causal network corresponding to the rules {BB->A,AAB->BAAB} (applied in a left-to-right scan) and initial condition ABAAB (Wolfram 2002, p. 498, fig. a).


The figure above shows the procedure for diagrammatically creating a causal network from a mobile automaton (Wolfram 2002, pp. 488-489).

In an evolution of a multiway system, each substitution event is a vertex in a causal network. Two events which are related by causal dependence, meaning one occurs just before the other, have an edge between the corresponding vertices in the causal network. More precisely, the edge is a directed edge leading from the past event to the future event.

Some causal networks are independent of the choice of evolution, and these are called causally invariant.

See also

Causal Invariance, Multiway System

Portions of this entry contributed by Todd Rowland

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Wolfram, S. A New Kind of Science. Champaign, IL: Wolfram Media, pp. 486-524, 2002.

Referenced on Wolfram|Alpha

Causal Network

Cite this as:

Rowland, Todd and Weisstein, Eric W. "Causal Network." From MathWorld--A Wolfram Web Resource.

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