17 citations · 93 across the 34 of their papers we have counts for
5 papers · 1 filter
Fractal Continuation
Michael F. Barnsley, Andrew Vince
A fractal function is a function whose graph is the attractor of an iterated function system. This paper generalizes analytic continuation of an analytic function to continuation o…
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…
A Combinatorial Characterization of the Critical Itineraries of a Uniform Dynamical System
Michael Barnsley, Wolfgang Steiner, Andrew Vince
For a function from the unit interval to itself with constant slope and one discontinuity, the itineraries of the point of discontinuity are called the critical itineraries. These…
The chaos game on a general iterated function system from a topological point of view
Michael F. Barnsley, Krzysztof Leśniak
We investigate combinatorial issues relating to the use of random orbit approximations to the attractor of an iterated function system with the aim of clarifying the role of the st…
On the continuity of the Hutchinson operator
Michael F. Barnsley, Krzysztof Leśniak
We investigate whether the Hutchinson operator associated with the iterated function system (IFS) is continuous. It clarifies several partial results scattered across recent litera…