Box-Counting Dimension Using Triangles
Tazeen Athar, Nayab Khalid, Shams Ul Islam
TL;DR
This paper introduces a new method for calculating the box-counting dimension using triangles, improving accuracy for fractals with rotation like the Bradley Spiral, and compares it with traditional methods.
Contribution
It proposes an alternative definition of the box-counting dimension that better captures the complexity of rotated fractals and provides a comparative analysis with existing methods.
Findings
Enhanced approximation for rotated fractals
Better fit for Bradley Spiral structure
Comparative analysis shows improved accuracy
Abstract
An alternate definition of the box-counting dimension is proposed, to provide a better approximation for fractals involving rotation such as the 'Bradley Spiral' structure. A curve fitting comparison of this definition with the box-counting dimension is also presented.
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Taxonomy
TopicsDigital Image Processing Techniques · Advanced Numerical Analysis Techniques · Computational Geometry and Mesh Generation