Fractal homeomorphism for bi-affine iterated function systems. (1st January 2013)

• Record Type: Journal Article
• Authors: Barnsley, Michael; Vince, Andrew
• Is Part Of: International journal of applied nonlinear science. Volume 1:Number 1(2013)
• Page Start: 3
• Page End: 19
• Publication Date: 2013-01-01
• Subjects: iterated function system -- fractal transformation -- bi-affine transformation; Science -- Mathematical models -- Periodicals; Engineering -- Mathematical models -- Periodicals; Nonlinear theories -- Periodicals; 501.5118
• Languages: English
• ISSNs: 1752-2862

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.