Fractal Interpolation Function is a novel method to construct irregular functions frominterpolation data. The talk will begin with a brief introduction of Fractals and differentkinds of Fractal Interpolation Functions. Then, I will intro duce a special kind of FractalInterpolation Function called “Super Fractal Interpolation Function” (SFIF) for finersimulation of the objects of the nature or outcomes of scientific experiments that revealone or more structures embedded into another (i.e. hybrid structures). We will lookat construction of SFIF wherein, an Iterated Function System (IFS) is chosen from apool of several IFS at each level of iteration leading to implementation of the desiredrandomness and variability in fractal interpolation of the given data. Further, I willdiscuss properties of integrability and differentiability of an SFIF. Finally, I will showa result on convergence of a Cubic Spline SFIF.
School of Mathematical Sciences
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