Lacunarity exponents

2018/06/03 by Michael Wilkinson, Marc Pradas, Greg Huber +1 · 3 citations
Decision Sciences · Engineering · Mathematics · Physics and Astronomy · #Fractal #Fractal dimension #Lacunarity #Mathematical analysis #Mathematics #Particle Dynamics in Fluid Flows #Physics #Probabilistic and Robust Engineering Design #Statistical physics #nlin.CD

paper · pdf · doi:10.1088/1751-8121/ab0349

published in Journal of Physics A Mathematical and Theoretical 52(11), 115101 (Institute of Physics) · 5 pages, 4 figures

arxiv created 2018/06/03 · openalex publication_date 2019/01/30 · arxiv updated 2019/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

Abstract Many physical processes result in very uneven, apparently random, distributions of matter, characterised by fluctuations of the local density varying over orders of magnitude. The density of matter in the sparsest regions can have a power-law distribution, with an exponent that we term the lacunarity exponent. We discuss a mechanism which explains the wide occurrence of these power laws, and give analytical expressions for the exponent in some simple models.

Citations

• Path coalescence transition and its applications
• Measuring the strangeness of strange attractors
• Fractal Geometry: Mathematical Foundations and Applications.
• Modeling Fractal Structure of City-Size Distributions Using Correlation Functions
• Scaling laws in the distribution of galaxies
• Uniformity transition for ray intensities in random media