Graph-directed fractal interpolation functions

Authors : Ali DENİZ, Yunus ÖZDEMİR

Pages : 829-840

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Publication Date : 0000-00-00

Article Type : Research Paper

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