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On Non-Tensor Product Bivariate Fractal Interpolation Surfaces on Rectangular Grids

1
Department of Computer Science and Biomedical Informatics, University of Thessaly, 35131 Lamia, Greece
2
Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, 157 84 Athens, Greece
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2020, 8(4), 525; https://doi.org/10.3390/math8040525
Received: 2 March 2020 / Revised: 25 March 2020 / Accepted: 27 March 2020 / Published: 3 April 2020
(This article belongs to the Special Issue Fractals: Geometry, Analysis and Mathematical Physics)
Some years ago, several authors tried to construct fractal surfaces which pass through a given set of data points. They used bivariable functions on rectangular grids, but the resulting surfaces failed to be continuous. A method based on their work for generating fractal interpolation surfaces is presented. Necessary conditions for the attractor of an iterated function system to be the graph of a continuous bivariable function which interpolates a given set of data are also presented here. Moreover, a comparative study for four of the most important constructions and attempts on rectangular grids is considered which points out some of their limitations and restrictions. View Full-Text
Keywords: attractor; bivariate surfaces; dynamic system; fractal interpolation; iterated function system attractor; bivariate surfaces; dynamic system; fractal interpolation; iterated function system
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Drakopoulos, V.; Manousopoulos, P. On Non-Tensor Product Bivariate Fractal Interpolation Surfaces on Rectangular Grids. Mathematics 2020, 8, 525.

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