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

Vasileios Drakopoulos and Polychronis Manousopoulos
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Vasileios Drakopoulos: Department of Computer Science and Biomedical Informatics, University of Thessaly, 35131 Lamia, Greece
Polychronis Manousopoulos: Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, 157 84 Athens, Greece

Mathematics, 2020, vol. 8, issue 4, 1-19

Abstract: 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.

Keywords: attractor; bivariate surfaces; dynamic system; fractal interpolation; iterated function system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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