Title: Fractal homeomorphism for bi-affine iterated function systems

Authors: Michael Barnsley; Andrew Vince

Addresses: Mathematical Sciences Institute, The Australian National University, Canberra, ACT 0200, Australia ' Department of Mathematics, University of Florida, 438 Little Hall, P.O. Box 118105, Gainesville, FL 32611-8105, USA

Abstract: The paper concerns fractal homeomorphism between the attractors of two bi-affine iterated function systems. After a general discussion of bi-affine functions, conditions are provided under which a bi-affine iterated function system is contractive, thus guaranteeing an attractor. After a general discussion of fractal homeomorphism, fractal homeomorphisms are constructed for a specific type of bi-affine iterated function system.

Keywords: iterated function systems; fractal transformation; bi-affine transformation; fractal homeomorphism.

DOI: 10.1504/IJANS.2013.052750

International Journal of Applied Nonlinear Science, 2013 Vol.1 No.1, pp.3 - 19

Received: 22 Aug 2012
Accepted: 11 Sep 2012
Published online: 30 Jul 2014 *

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