Sums of convex compacta as attractors of hyperbolic IFS's

Abstract

We prove that a finite union of convex compacta in $\mathbb{R}^n$ may be represented as the attractor of a hyperbolic IFS. If such a union is the condensation set for some hyperbolic IFS with condensation, then its attractor can be represented as the attractor of a standard hyperbolic IFS. We illustrate this result with the hyperbolic IFS with condensation, whose attractor is the well-known ``The Pythagoras tree'' fractal.