arXiv subjects
Publications and source records attributed to Michael F Barnsley.
The theory of fractal tilings of fractal blow-ups is extended to graph-directed iterated function systems, resulting in generalizations and extensions of some of the theory of Anderson and Putnam and of Bellisard et al. regarding self-similar tilings.
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.