Butterfly diffusion over sparse point sets

František Gašpar and Jaromír Kukal

Physica A: Statistical Mechanics and its Applications, 2024, vol. 646, issue C

Abstract: The graph-based random walk model of fractal diffusion is limited in its use to the connected sets and does not allow for direct fractal dimension estimation based on observed data. We discuss a task of directly obtaining accurate fractal dimension estimates and propose butterfly diffusion as an alternative approach using an explicit relation between walk and fractal dimensions. The validity of the presented approach is evaluated and statistical properties of the dimension estimates are presented. Through experiments on self-similar sets, we demonstrate the effectiveness of this approach in producing unbiased dimension estimates, offering a promising tool for fractal analysis and Monte Carlo simulations. The estimate of fractal dimension can be also created from spectral dimension, but this approach is less general and less accurate.

Keywords: Dimension estimation; Fractal dimension; Point set; Resistance scaling; Walk dimension (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437124004023
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:646:y:2024:i:c:s0378437124004023

DOI: 10.1016/j.physa.2024.129893

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().