Geodesic
Fractal Interpolation in Creating Prefractal Images
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 {[xi yi zi]T , i = 0, 1,..., n} so that f (xi) = [ yi 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.
Classification : 28A80 
@article{VM_2000_2_2_a0,
     author = {Ljubi\v{s}a M. Koci\'c and Alba Chiara Simoncelli},
     title = {Fractal {Interpolation} in {Creating} {Prefractal} {Images}},
     journal = {Visual Mathematics},
     publisher = {mathdoc},
     volume = {2},
     number = {2},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VM_2000_2_2_a0/}
}
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AU  - Ljubiša M. Kocić
AU  - Alba Chiara Simoncelli
TI  - Fractal Interpolation in Creating Prefractal Images
JO  - Visual Mathematics
PY  - 2000
VL  - 2
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VM_2000_2_2_a0/
LA  - en
ID  - VM_2000_2_2_a0
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%A Alba Chiara Simoncelli
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%J Visual Mathematics
%D 2000
%V 2
%N 2
%I mathdoc
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%G en
%F VM_2000_2_2_a0
Ljubiša M. Kocić; Alba Chiara Simoncelli. Fractal Interpolation in Creating Prefractal Images. Visual Mathematics, Tome 2 (2000) no. 2. http://geodesic.mathdoc.fr/item/VM_2000_2_2_a0/