Construction of Fractal Surfaces by Recurrent Fractal Interpolation Curves
Chol-hui Yun, Hyong-chol O., Hui-chol Choi
TL;DR
This paper introduces a novel method for constructing fractal surfaces using recurrent fractal curves and Lipschitz functions, providing a flexible approach with dimension estimation.
Contribution
It presents a new technique combining recurrent fractal curves and Lipschitz functions for constructing fractal surfaces with dimension analysis.
Findings
Constructed fractal surfaces using recurrent fractal curves.
Estimated box-counting dimensions of the surfaces.
Combined methods for more flexible surface construction.
Abstract
A method to construct fractal surfaces by recurrent fractal curves is provided. First we construct fractal interpolation curves using a recurrent iterated functions system(RIFS) with function scaling factors and estimate their box-counting dimension. Then we present a method of construction of wider class of fractal surfaces by fractal curves and Lipschitz functions and calculate the box-counting dimension of the constructed surfaces. Finally, we combine both methods to have more flexible constructions of fractal surfaces.
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