The Liar paradox is a familiar sentence that asserts its own falsehood
. Just slightly less familiar is the Dualist, involving a pair of mutu
ally referential sentences. Here we consider variations on the Dualist
and Triplist, modelling their dynamical semantics using iteration wit
hin an infinite-valued logic. Strange attractors and fractal escape-ti
me diagrams appear in two dimensions for the Dualist and in three dime
nsions for the Triplist.