  New tilings of certain subsets of $\mathbb{R}^{M}$ are studied, tilings
associated with fractal blow-ups of certain similitude iterated function
systems (IFS). For each such IFS with attractor satisfying the open set
condition, our construction produces a usually infinite family of tilings that
satisfy the following properties: (1) the prototile set is finite; (2) the
tilings are repetitive (quasiperiodic); (3) each family contains
self-similartilings, usually infinitely many; and (4) when the IFS is rigid in
an appropriate sense, the tiling has no non-trivial symmetry; in particular the
tiling is non-periodic.
