17 citations · 64 across the 22 of their papers we have counts for
28 papers
Transition Phenomena for the Attractor of an Iterated Function System
Krzysztof Leśniak, Nina Snigireva, Filip Strobin +1
Iterated function systems (IFSs) and their attractors have been central to the theory of fractal geometry almost from its inception. And contractivity of the functions in the IFS h…
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…
The Average Size of a Connected Vertex Set of a -connected Graph
Andrew Vince
The topic is the average order of a connected induced subgraph of a graph . This generalizes, to graphs in general, the average order of a subtree of a tree. In 1984, Jam…
A Lower Bound on the Average Size of a Connected Vertex Set of a Graph
Andrew Vince
The topic is the average order of a connected induced subgraph of a graph. This generalizes, to graphs in general, the average order of a subtree of a tree. In 1984, Jamison proved…
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…
Thresholds for One-Parameter Families of Affine Iterated Function Systems
Andrew Vince
This paper examines thresholds for certain properties of the attractor of a general one-parameter affine family of iterated functions systems. As the parameter increases, the itera…