Abstract Let $\{X_n\}_{n\in{\mathbb{N}}}$ be an ${\mathbb{X}}$ -valued iterated function system (IFS) of Lipschitz maps defined as $X_0 \in {\mathbb{X}}$ and for $n\geq 1$ , $X_n\;:\!=\;F(X_{n-1},\vartheta_n)$ where $\{\vartheta_n\}_{n \ge 1}$ are independent identically distributed random variables with common probability distribution $\mathfrak{p}$ $F(\cdot,\cdot)$ is continuous in the first ...

In this paper, the question of which compact metric spaces can be attractors of hyperbolic iterated function systems on Euclidean space is studied. It is shown that given any finite-dimensional compact metric X , there is a Cantor set C such that the disjoint union of C and X is an attractor. In the process, it is proved that every such X is the Lipschitz image of a Cantor set.

This article presents an implementation of the Fractal Flames algorithm. It uses CUDA and OpenGL to take advantage of the computational power of modern graphics cards. GPUs use a SIMT (Single Instruction Multiple Thread) architecture. It is needed to design programs in a way which avoids divergent branching. The Fractal Flames algorithm involves random function selection which needs to be calcu...

Boundary Controlled Iterated Function Systems is a new layer of control over traditional (linear) IFS, allowing creation of a wide variety of shapes. In this work, we demonstrate how subdivision schemes may be generated by means of Boundary Controlled Iterated Function Systems, as well as how we may go beyond the traditional subdivision schemes to create free-form fractal shapes. BC-IFS is a po...