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The chaos game on a general iterated function system

Published online by Cambridge University Press:  13 September 2010

MICHAEL F. BARNSLEY  and
ANDREW VINCE
MICHAEL F. BARNSLEY
Affiliation:
Department of Mathematics, Australian National University, Canberra, ACT, Australia (email: [email protected])
ANDREW VINCE
Affiliation:
Department of Mathematics, University of Florida, Gainesville, FL 32611-8105, USA (email: [email protected])
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Abstract

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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 31 , Issue 4 , August 2011 , pp. 1073 - 1079
Copyright
Copyright © Cambridge University Press 2010

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