Analytical procedure to determine the self-referred lacunarity function for simple shapes. Supplementary material

TL;DR

This paper provides an analytical method to calculate the self-referred lacunarity for simple shapes, serving as a validation tool for computational algorithms in shape analysis.

Contribution

It introduces detailed analytical calculations for the self-referred lacunarity of basic shapes, enhancing validation standards for computational methods.

Findings

Analytical formulas for lacunarity of a square and a cross.

Validation benchmarks for computational lacunarity algorithms.

Enhanced accuracy in shape analysis validation.

Abstract

The analytical calculation of the self-referred lacunarity is used as a validation standard of the computational algorithm. In this supplementary material to our article (see cond-mat/0407079) we present a detailed calculation for two simple shapes, namely a square box and a cross.