Construction and box dimension of recurrent fractal interpolation surfaces
Zhen Liang, Huo-Jun Ruan
TL;DR
This paper introduces a flexible framework for constructing recurrent fractal interpolation surfaces on grids, focusing on bilinear RFISs and analyzing their box dimension under specific conditions.
Contribution
It presents a general construction method for RFISs, introduces bilinear RFISs without restrictions, and derives their box dimension under certain assumptions.
Findings
Bilinear RFISs are easy to generate.
Box dimension of bilinear RFISs is obtained under uniform sum conditions.
Framework allows flexible construction of fractal surfaces.
Abstract
In this paper, we present a general framework to construct recurrent fractal interpolation surfaces (RFISs) on rectangular grids. Then we introduce bilinear RFISs, which are easy to be generated while there are no restrictions on interpolation points and vertical scaling factors. We also obtain the box dimension of bilinear RFISs under certain constraints, where the main assumption is that vertical scaling factors have uniform sums under a compatible partition.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Numerical Analysis Techniques · Computer Graphics and Visualization Techniques