An effective method to compute the box-counting dimension based on the mathematical definition and intervals

Abstract

Fractal dimension is an appropriate indicator to describe the complexity of a certain geometry, and box-counting analysis is proved to be an effective and appropriate method for fractal dimension estimation which is widely used. However, traditional box-counting methods based on images may not always accurate especially in small box scale due to the restriction of pixels. This paper aims to introduce a method based on generating fractal and determining boxes by rigid mathematical definition to eliminate the deviation of each box scale and to carry out more dependable results. Several samples of the simple and recursive fractal are analyzed to verify the accuracy of the box-counting method based on mathematical definition and interval in this paper.