Fractal Dimension Computation From Equal Mass Partitions

TL;DR

This paper compares two mass-oriented methods for computing the generalized dimension of multifractal sets, demonstrating their effectiveness where traditional box-counting methods often fail, and discusses their strengths and limitations.

Contribution

It introduces and evaluates two mass-oriented methods for generalized dimension computation, showing their advantages over box-counting in certain cases.

Findings

Mass-oriented methods produce better results than box-counting for some multifractal sets.

Both methods are effective in cases where box-counting fails.

The paper discusses the strengths and limitations of each method.

Abstract

While the numerical methods which utilizes partitions of equal-size, including the box-counting method, remain the most popular choice for computing the generalized dimension of multifractal sets, two mass- oriented methods are investigated by applying them to the one-dimensional generalized Cantor set. We show that both mass-oriented methods generate relatively good results for generalized dimensions for important cases where the box-counting method is known to fail. Both the strengths and limitations of the methods are also discussed.