Fractal Interpolation in Creating Prefractal Images
Ljubisa M. Kocic^{1}
and
Alba Chiara Simoncelli^{2}
^{1}Faculty of Electronic Engrg., Univ. Nis
Nis, Yugoslavia
^{2}Dip. Matematica ed Appl., Univ. Federico II
Napoli, Italy
kocic@elfak.ni.ac.yu
simoncel@matna2.dma.unina.it
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®
R^{2}
interpolating the data set {[x_{i } y_{i }
z_{i}]^{T }, i = 0, 1,..., n}
so that f (x_{i}) = [ y_{i }
z_{i}]^{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 lowertriangular 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.
