A multiway system that generates causal graphs which are all isomorphic as acyclic digraphs is said to exhibit causal invariance, and the causal graph itself is also said to be causally invariant. Essentially, causal invariance means that no matter which evolution is chosen for a system, the history is the same in the sense that the same events occur and they have the same causal relationships. The figures above illustrate two nontrivial substitution systems that exhibit the same causal graphs independent of the order in which the rules are applied.
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