Algorithms generating images of attractors of generalized iterated function systems

TL;DR

This paper develops algorithms for generating images of attractors of generalized iterated function systems, extending classical methods to more complex systems and specialized affine cases.

Contribution

It introduces new algorithms for visualizing attractors of generalized iterated function systems, including adaptations for affine systems, expanding computational tools in fractal geometry.

Findings

Algorithms successfully generate attractor images for GIFS

Classical and chaos game algorithms adapted for GIFS

Specialized algorithms for affine GIFS introduced

Abstract

The paper is devoted to searching algorithms which will allow to generate images of attractors of \emph{generalized iterated function systems} (GIFS in short), which are certain generalization of classical iterated function systems, defined by Mihail and Miculescu in 2008, and then intensively investigated in the last years (the idea is that instead of selfmaps of a metric space $X$, we consider mappings form the Cartesian product $X\times...\times X$ to $X$). Two presented algorithms are counterparts of classical \emph{deterministic algorithm} and so-called \emph{chaos game}. The third and fourth one one is fitted to special kind of GIFSs - to \emph{affine} GIFS, which are, in turn, also investigated.