The chaos game on a general iterated function system from a topological point of view

Abstract

We investigate combinatorial issues relating to the use of random orbit approximations to the attractor of an iterated function system with the aim of clarifying the role of the stochastic process during generation the orbit. A Baire category counterpart of almost sure convergence is presented; and a link between topological and probabilistic methods is observed.

The proof of the main theorem in the older version contained an error. The new proof works under stronger hypotheses put on the structure of the attractor

Cited by in corpus (3)

• Fast Basins and Branched Fractal Manifolds of Attractors of Iterated Function Systems
• Density of fiberwise orbits in minimal iterated function systems on the circle
• Random iteration and projection method