The Iterated Function System (IFS) used in the construction of Coalescence Hidden-variable Fractal Interpolation Function (CHFIF) depends on the interpolation data. The insertion of a new point in a given set of interpolation data is called the problem of node insertion. In this paper, the effect of insertion of new point on the related IFS and the Coalescence Fractal Interpolation Function is studied. Smoothness and Fractal Dimension of a CHFIF obtained with a node are also discussed.

Node insertion in Coalescence Fractal Interpolation Function

The Iterated Function System(IFS) used in the construction of Coalescence Hidden-variable Fractal Interpolation Function depends on the interpolation data. In this note, the effect of insertion of data on the related IFS and the Coalescence Hidden-variable Fractal Interpolation Function is studied.

Data Variation in Coalescence Fractal Interpolation Function

A fractal interpolant of the proper interpolation data is fully determined by the functional equation of Read- Bejraktarevic type and a free vertical scaling vector ν such that ||ν|| < 1. In this note, it is shown how insertion of the data impacts the related Read-Bejraktarevic equation and the interpolant. Some examples support the theory.

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Ljubiša M. Kocić

Papers

Data variation in fractal interpolation