Fractal Interpolation in Creating Prefractal Images

Ljubisa M. Kocic1
Alba Chiara Simoncelli2

1Faculty of Electronic Engrg., Univ. Nis
Nis, Yugoslavia
2Dip. Matematica ed Appl., Univ. Federico II
Napoli, Italy

Abstract: The Iterated Function System (IFS) is a constructive way to define vector valued fractal interpolation functions for a given set  of interpolation data. This paper deals with the special case of  an IFS that constructs the graph of a continuous vector valued function  f : R® R2 interpolating the data set {[x y zi]T , i = 0, 1,..., n} so that  f (xi) = [ y zi]T  i = 0, 1,..., n. Its behavior under affine transformation of the interpolation data is examined. Particularly, conditions are given under which vector valued fractal interpolation functions are affine invariant  upon some  classes of affine mappings whose linear part is given by a lower-triangular matrix of special form or a block diagonal matrix.  Some  visual effects created by prefractals associated to the graphs of vector valued fractal interpolation functions are examined.