Fractal Homeomorphism for Bi-affine Iterated Function Systems
Michael Barnsley, Andrew Vince
TL;DR
This paper explores conditions for fractal homeomorphisms between attractors of bi-affine iterated function systems, providing theoretical foundations and constructing specific examples of such homeomorphisms.
Contribution
It introduces conditions for contractiveness of bi-affine IFS and constructs fractal homeomorphisms for a specific class of these systems.
Findings
Conditions for contractiveness of bi-affine IFS established
Fractal homeomorphisms constructed for specific bi-affine IFS
Theoretical framework for bi-affine fractal homeomorphisms developed
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.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Chaos control and synchronization · Cellular Automata and Applications