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Construction of recurrent bivariate fractal interpolation surfaces and computation of their box-counting dimension |
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| Authors: | P. Bouboulis Leoni Dalla V. Drakopoulos |
| Affiliation: | aDepartment of Informatics and Telecommunications, Telecommunications and Signal Processing, University of Athens, Panepistimioupolis 157 84, Athens, Greece;bDepartment of Mathematics, Mathematical Analysis, University of Athens, Panepistimioupolis 157 84, Athens, Greece;cDepartment of Informatics and Telecommunications, Theoretical Informatics, University of Athens, Panepistimioupolis 157 84, Athens, Greece |
| Abstract: | Recurrent bivariate fractal interpolation surfaces (RBFISs) generalise the notion of affine fractal interpolation surfaces (FISs) in that the iterated system of transformations used to construct such a surface is non-affine. The resulting limit surface is therefore no longer self-affine nor self-similar. Exact values for the box-counting dimension of the RBFISs are obtained. Finally, a methodology to approximate any natural surface using RBFISs is outlined. |
| Keywords: | Fractal interpolation functions IFS RIFS Fractals Bivariate fractal interpolation surfaces Box-counting dimension Minkowski dimension |
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