Limit sets of graph-driven iterated (multi)function systems

Abstract. Our paper focuses on a new approach to the construction of graph sequences driven using iterated function systems (briefly IFSs) and iterated multifunction systems (briefly IMSs). We build self-similar graphs sequences generated initally based on an arbitrary graph. We analyze the graphs sequences gotten within the iterations of IFSs and IMSs. We specially analyze the density properties between those graphs which are in the same sequence and we also focus on graph sequences driven by Erdős-Rényi graphs.
The main aim of our paper is to analyze the limit sets of the graph-driven IFSs and IMSs. We characterize them using the Sierpinski carpet and the \([0,1]^2\) set which we interpret as limits of the constructed graph sequences.