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The top-selling multimedia encyclopedia Encarta, published by Microsoft Corporation, includes on one CD-ROM seven thousand color photographs which may be viewed interactively on a computer screen. The images are diverse; they are of buildings, musical instruments, people’s faces, baseball bats, ferns, etc. What most users do not know is that all of these… (More)

- Michael F. Barnsley, Valerie Ervin, Douglas P. Hardin, Jude Lancaster
- Proceedings of the National Academy of Sciences…
- 1986

The problem of providing succinct approximate descriptions of given bounded subsets of R(n) can be solved by application of the contraction mapping principle.

- Michael F. Barnsley, Arnaud Jacquin, Francois Malassenet, Laurie Reuter, Alan D. Sloane
- SIGGRAPH
- 1988

Chaotic dynamics can be used to model shapes and render textures in digital images. This paper addresses the problem of how to model geometrically shapes and textures of two dimensional images using iterated function systems. The successful solution to this problem is demonstrated by the production and processing of synthetic images encoded from color… (More)

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 with a natural probability distribution. These V -variable fractals… (More)

- Michael F. Barnsley
- The American Mathematical Monthly
- 2009

The main theorem of this paper establishes conditions under which the ‘chaos game’ algorithm almost surely yields the attractor of an iterated function system. The theorem holds in a very general setting, even for non-contractive iterated function systems, and under weaker conditions on the random orbit of the chaos game than obtained previously.

This paper contains four main results associated with an attractor of a projective iterated function system (IFS). The first theorem characterizes when a projective IFS has an attractor which avoids a hyperplane. The second theorem establishes that a projective IFS has at most one attractor. In the third theorem the classical duality between points and… (More)

- Michael F. Barnsley, Andrew Vince
- Discrete & Computational Geometry
- 2014

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 literature in ad hoc ways, as well as new examples, can be constructed by this method. These tilings can be used to extend a fractal transformation defined on the attractor of a… (More)