Graph-directed fractal interpolation functions

Authors: ALİ DENİZ, YUNUS ÖZDEMİR

Abstract: It is known that there exists a function interpolating a given data set such that the graph of the function is the attractor of an iterated function system, which is called a fractal interpolation function. We generalize the notion of the fractal interpolation function to the graph-directed case and prove that for a finite number of data sets there exist interpolation functions each of which interpolates a corresponding data set in $\mathbb{R}^2$ such that the graphs of the interpolation functions are attractors of a graph-directed iterated function system.

Keywords: Fractal interpolation function, iterated function system, graph-directed iterated function system

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