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arXiv · 1404.1300

A construction of fractal surfaces with function scaling factors on a rectangular grid

Chol-Hui Yun·Hui-Chol Choi·Hyong-Chol O
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Abstract

A fractal surface is a set which is a graph of a bivariate continuous function. In the construction of fractal surfaces using IFS, vertical scaling factors in IFS are important one which characterizes a fractal feature of surfaces constructed. We construct IFS with function vertical scaling factors which are 0 on the boundaries of a rectangular grid using arbitrary data set on a rectangular grid and give a condition for an attractor of the IFS constructed being a surface. Finally, lower and upper bounds of Box-counting dimension of the constructed surface are estimated.

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Chol-Hui Yun, Hui-Chol Choi, Hyong-Chol O. 2014-04-03. A construction of fractal surfaces with function scaling factors on a rectangular grid. https://arxiv.org/abs/1404.1300

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