17 citations · 93 across the 34 of their papers we have counts for
24 papers · 1 filter
Tilings from Tops of Overlapping Iterated Function Systems
Michael F. Barnsley, Corey de Wit
The top of the attractor of a hyperbolic iterated function system is defined and used to extend s…
Elementary fractal geometry. 5. Weak separation is strong separation
Christoph Bandt, Michael F. Barnsley
For self-similar sets, there are two important separation properties: the open set condition and the weak separation condition introduced by Zerner, which may be replaced by the fo…
Blowups and Tops of Overlapping Iterated Function Systems
Louisa F. Barnsley, Michael F. Barnsley
We review aspects of an important paper by Robert Strichartz concerning reverse iterated function systems (i.f.s.) and fractal blowups. We compare the invariant sets of reverse i.f…
Central Open Sets Tilings
Louisa Barnsley, Michael Barnsley
We introduce a method for constructing collections of subsets of , using an iterated function system, a set and a cost function. We refer to these collections…
Distortion Reversal in Aperiodic Tilings
Louisa Barnsley, Michael Barnsley, Andrew Vince
It is proved that homeomorphic images of certain two-dimensional aperiodic tilings, such as Ammann-A2 tilings, are recognizable, in both mathematical and practical senses. One impl…
Tiling Iterated Function Systems
Michael F. Barnsley, Louisa F. Barnsley, Andrew Vince
This paper presents a detailed symbolic approach to the study of self-similar tilings. It uses properties of addresses associated with graph-directed iterated function systems to e…