# Multifractal Modeling and Lacunarity Analysis

@article{Cheng1997MultifractalMA, title={Multifractal Modeling and Lacunarity Analysis}, author={Qiuming Cheng}, journal={Mathematical Geology}, year={1997}, volume={29}, pages={919-932} }

The so-called “gliding box method” of lacunarity analysis has been investigated for implementing multifractal modeling in comparison with the ordinary box-counting method. Newly derived results show that the lacunarity index is associated with the dimension (codimension) of fractal, multifractal and some types of nonfractals in power-law relations involving box size; the exponent of the lacunarity function corresponds to the fractal codimension (E – D) for fractals and nonfractals, and to the…

## 92 Citations

On Lacunarity Analysis

- Mathematics
- 2002

The notion of Lacunarity has been originally introduced by Mandelbrot, in a broad way, to stress the fact that fractals of the same dimension can have quite different appearance. This vague concept…

Lacunarity Analysis of Fracture Intensity Maps: Are they Multifractals?

- Geology
- 2016

Lacunarity (L) is a scale (r)-dependent parameter that was developed for quantifying clustering in fractals and has subsequently been employed to characterize various natural patterns. It has been…

LACUNARITY ANALYSES OF MULTIFRACTAL AND NATURAL GRAYSCALE PATTERNS

- Computer Science
- 2014

Lacunarity (L) is a scale (r)-dependent parameter that was developed for quantifying clustering in fractals and has subsequently been employed to characterize various natural patterns and was used in discriminating between multifractal grayscale patterns with the same D2 values, but different degrees of scale-dependent clustering.

Detection of dynamical regime transitions with lacunarity as a multiscale recurrence quantification measure

- PhysicsNonlinear Dynamics
- 2020

We propose lacunarity as a novel recurrence quantification measure and illustrate its efficacy to detect dynamical regime transitions which are exhibited by many complex real-world systems. We carry…

Comparison of gliding box and box-counting methods in river network analysis

- Environmental Science
- 2007

Abstract. We use multifractal analysis to estimate the Renyi dimensions of river basins by two different partition methods. These methods differ in the way that the Euclidian plane support of the…

A novel iterative approach for mapping local singularities from geochemical data

- Geology
- 2007

There are many phenomena in nature, such as earthquakes, landslides, floods, and large-scale mineralization that are characterized by singular functions exhibiting scale invariant properties. A local…

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