A multiway system is a kind of substitution system in which multiple states are permitted at any stage. This accommodates rule systems in which there is more than one possible way to perform an update.
A simple example is a string substitution system. For instance, take the rules 
and the initial condition 
. There are two choices for how to proceed. Applying the
first rule yields the evolution 
, while applying the second rule yields the evolution
. So at the first step,
there is a single state (
), at the second step there are two states 
, and at the third step there is a single state 
.
A path through a multiway system arising from a choice of which substitutions to make is called an evolution. Typically, a multiway system will have a large number
of possible evolutions. For example, consider strings of 
s and 
s with the rule 
. Then most strings will have more than one occurrence
of the substring 
,
and each occurrence leads down another path in the multiway system.
