Blending attractors of Iterated Function Systems

2025/10/16 by Oliveira, Elismar R.
#Dynamical Systems (math.DS) #FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.2510.14474

Abstract

In this paper we discuss a new method to blend fractal attractors using the code map for the IFS formed by the Hutchinson--Barnsley operators of a finite family of hyperbolic IFSs. We introduce a parameter called blending coefficient to measure the similarity between the blended set and each one of the original attractors. We also introduce a discrete approximation algorithm and prove a rigorous error estimation used to approximate these new objects. Several simulation results are provided illustrating our techniques.

Citations

• Fractal Attractors in Random Nonlinear Iterated Function Systems: Existence, Stability, and Dimensional Properties
• A multiresolution algorithm to generate images of generalized fuzzy\n fractal attractors
• Attractors of sequences of iterated function systems
• The Ergodic Theorem for a new kind of attractor of a GIFS

Related

• Transformations between attractors of hyperbolic iterated function systems
• Fractal Tiling
• Attractors of sequences of function systems and their relation to\n non-stationary subdivision
• Redefining fractals by Suzuki contraction
• Inhomogeneous attractors and box dimension