The quantization dimension function for an F -conformal measure mF generated by an infinite conformal iterated function system satisfying the strong open set condition and by a summable Hölder family of functions is expressed by a simple formula involving the temperature function of the system. The temperature function is commonly used to perform a multifractal analysis, in our context of the m...

The main theorem of this paper establishes conditions under which the ‘chaos game’ algorithm almost surely yields the attractor of an iterated function system. The theorem holds in a very general setting, even for non-contractive iterated function systems, and under weaker conditions on the random orbit of the chaos game than obtained previously.

We consider iterated function systems on the interval with random perturbation. Let Yε be uniformly distributed in [1 − ε, 1 + ε] and let fi ∈ C be contractions with fixpoints ai. We consider the iterated function system {Yεfi + ai(1− Yε)}i=1, were each of the maps are chosen with probability pi. It is shown that the invariant density is in L and the L-norm does not grow faster than 1/ √ ε, as ...

We study special infinite iterated function systems derived from complex continued fraction expansions with restricted entries. We focus our attention on the corresponding limit set whose Hausdorff dimension will be denoted by h. Our primary goal is to determine whether the h-dimensional Hausdorff and packing measure of the limit set is positive and finite. 1. Preliminaries The theory of unifor...

Iterated function systems with contracting functions have been widely applied in contexts relating art and science. This paper explores iterated function systems which consist of expanding linear functions. An area in the plane is divided in parts which are defined implicitly by an inverse function technique. With each part, an expanding function is associated. A coloring technique is proposed ...