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 
(applied in a left-to-right scan) and initial condition 
(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.
