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The Study on Bivariate Fractal Interpolation Functions and Creation of Fractal Interpolated Surfaces

Heping Xie, Hongquan Sun

Open publisher page 108 citations

Abstract

In this paper, the methods of construction of a fractal surface are introduced, the principle of bivariate fractal interpolation functions is discussed. The theorem of the uniqueness of an iterated function system of bivariate fractal interpolation functions is proved. Moreover, the theorem of fractal dimension of fractal interpolated surface is derived. Based on these theorems, the fractal interpolated surfaces are created by using practical data.

About this research paper

What this paper is about

In this paper, the methods of construction of a fractal surface are introduced, the principle of bivariate fractal interpolation functions is discussed. The theorem of the uniqueness of an iterated function system of bivariate fractal interpolation functions is proved. Moreover, the theorem of fractal dimension of fractal interpolated surface is derived. Based on these theorems, the fractal interpolated surfaces are created by using practical data.

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OpenAlex reports 108 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper, the methods of construction of a fractal surface are introduced, the principle of bivariate fractal interpolation functions is discussed. The theorem of the uniqueness of an iterated function system of bivariate fractal interpolation functions is proved. Moreover, the theorem of fractal dimension of fractal interpolated surface is derived. Based on these theorems, the fractal interpolated surfaces are created by using practical data.

Key concepts: Fractal, Iterated function system, Mathematics, Interpolation (computer graphics), Fractal derivative, Fractal dimension on networks, Fractal dimension, Bivariate analysis

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