Tilings from Graph Directed Iterated Function Systems
Metric Geometry
2019-12-06 v1 Combinatorics
Dynamical Systems
Abstract
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.
Cite
@article{arxiv.1912.02587,
title = {Tilings from Graph Directed Iterated Function Systems},
author = {Michael Barnsley and Andrew Vince},
journal= {arXiv preprint arXiv:1912.02587},
year = {2019}
}