The Study of Local Dimension of Fractals Using Projection Method
Date Issued
2007
Date
2007
Author(s)
Chen, Hung-Chen
DOI
zh-TW
Abstract
In fractal geometry, fractal dimension is an important number that describes the characteristic of fractals. The study about definition and applications of fractal dimension is well established already. However, we have no idea about the local directions of fractals when we use fractal dimension for analysis. For this reason, we develop some tools that can help us find the local directions of fractals. As well, using the projection method, we define some local dimensions of fractal along each direction to replace a single global fractal dimension. The local dimensions can help us understand the details of the structure and its differences along different directions.
In this paper, we analyze two famous fractals: Henon map and Lorenz attractor. We calculate the projected dimensions along different directions. Consistency of eigen-directions, uniformity of distribution, and numerical error of them are also discussed.
Subjects
碎形
局部維度
投影法
奇異值分解
共變異矩陣
fractal
local dimension
projection
singular value decomposition
covarience matrix
Type
thesis
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