Up to equivalence, a substitution in propositional logic is an
endomorphism of its free algebra. On the dual space, this results in a
continuous function, and whenever the space carries a natural measure
one may ask about the stochastic properties of the action. In
classical logic there is a strong dichotomy: while over finitely many
propositional variables everything is trivial, the study of the
continuous transformations of the Cantor space is the subject of an
extensive literature, and is far from being a completed task. In
many-valued logic this dichotomy disappears: already in the
finite-variable case many interesting phenomena occur, and the present
paper aims at displaying some of these.