  A new method for constructing self-referential tilings of Euclidean space
from a graph directed iterated function system, based on a combinatorial
structure we call a pre-tree, is introduced. In the special case that we refer
to as balanced, the resulting tilings have a finite set of prototiles, are
quasiperiodic but not periodic, and are self-similar. A necessary and
sufficient condition for two balanced tilings to be congruent is provided.
