17 citations · 93 across the 34 of their papers we have counts for
8 papers · 1 filter
Tilings from Graph Directed Iterated Function Systems
Michael Barnsley, Andrew Vince
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…
Self-Similar Polygonal Tiling
Michael Barnsley, Andrew Vince
The purpose of this paper is to give the flavor of the subject of self-similar tilings in a relatively elementary setting, and to provide a novel method for the construction of suc…
Chaos game for IFSs on topological spaces
Michael F. Barnsley, Krzysztof Lesniak, Miroslav Rypka
We explore the chaos game for the continuous IFSs on topological spaces. We prove that the existence of attractor allows us to use the chaos game for visualization of attractor. Th…
Fractal Tiling
Michael Barnsley, Andrew Vince
A simple, yet unifying method is provided for the construction of tilings by tiles obtained from the attractor of an iterated function system (IFS). Many examples appearing in the…
Numerics and Fractals
Michael F. Barnsley, Markus Hegland, Peter Massopust
Local iterated function systems are an important generalisation of the standard (global) iterated function systems (IFSs). For a particular class of mappings, their fixed points ar…
Bilinear Fractal Interpolation and Box Dimension
Michael F. Barnsley, Peter R. Massopust
In the context of general iterated function systems (IFSs), we introduce bilinear fractal interpolants as the fixed points of certain Read-Bajraktarević operators. By exhibiting a…