V -variable fractals: Fractals with partial self similarity ✩

By Michael F. Barnsley, John E. Hutchinson, Orjan Stenflo. 2008

99 citations recorded by the source corpus.

We establish properties of a new type of fractal which has partial self similarity at all scales. For any collection of iterated functions systems with an associated probability distribution and any positive integer V there is a corresponding class of V-variable fractal sets or measures. These V-variable fractals can also be obtained from the points on the attractor of a single deterministic iterated function system. Existence, uniqueness and approximation results are established under average contractive assumptions. We also obtain extensions of some basic results concerning iterated function systems.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a5f9b620d1cb78885f93125526d5b0a2786a8c8f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. Andrew Vince
2. Michael F. Barnsley
3. Orjan Stenflo

In Statistical and Nonlinear Physics

1. Andrew Vince
2. Orjan Stenflo

Citations in the corpus

• The chaos game on a general iterated function system (2010, background): “Consistent with the terminology in [5], [6], [7], an attractor of such an IFS F is called a superfractal.”
• A survey of average contractive iterated function systems (2012, background): “[7], we proved the following theorem:”