具有垂直缩放功能的分形插值面的盒尺寸

Fractals Pub Date : 2024-04-20 DOI:10.1142/s0218348x24500713

LAI JIANG

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引用次数: 0

摘要

在本文中，我们首先提出了一个简单的 Lemma，它允许我们通过相关的振荡和与振荡向量来估计给定函数图形的盒维度。然后，我们定义了广义仿射分形插值面（FIS）的垂直缩放矩阵。通过使用这些矩阵，我们建立了不同层次振荡向量之间的关系，从而使我们能够在一定的约束条件下获得广义仿射分形插值面的箱体维度。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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BOX DIMENSION OF FRACTAL INTERPOLATION SURFACES WITH VERTICAL SCALING FUNCTION

In this paper, we first present a simple lemma which allows us to estimate the box dimension of graphs of given functions by the associated oscillation sums and oscillation vectors. Then we define vertical scaling matrices of generalized affine fractal interpolation surfaces (FISs). By using these matrices, we establish relationships between oscillation vectors of different levels, which enables us to obtain the box dimension of generalized affine FISs under certain constraints.

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Fractals

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