# Determination of fractal dimensions for geometrical multifractals

@article{Tl1989DeterminationOF, title={Determination of fractal dimensions for geometrical multifractals}, author={Tam{\'a}s T{\'e}l and Agnes Fulop and Tam{\'a}s Vicsek}, journal={Physica A-statistical Mechanics and Its Applications}, year={1989}, volume={159}, pages={155-166} }

## 140 Citations

### Characterizing the lacunarity of random and deterministic fractal sets.

- MathematicsPhysical review. A, Atomic, molecular, and optical physics
- 1991

The lacunarity of a set is defined from the fluctuations of the mass distribution function, which is found using an algorithm the authors call the gliding-box method, and this definition is applied to characterize the geometry of random and deterministic fractal sets.

### Fractal dimension computation from equal mass partitions.

- PhysicsChaos
- 2014

Two mass-oriented methods for computing generalized dimensions of multifractal sets are revisited and their strengths and limitations are discussed.

### Multifractal portrayal of the Swiss population

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Fractal geometry is a fundamental approach for describing the complex irregularities of the spatial structure of point patterns. The present research characterizes the spatial structure of the Swiss…

### A precise characterization of three-dimensional percolating backbones

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- 1994

The backbones of three-dimensional critical percolation clusters are extracted and the fractal dimension is accurately calculated using various mass-scaling and box-counting techniques to be…

### Generalized Dimensions and Multifractals

- Mathematics
- 2020

In the preceding two chapters, we studied the information dimension dI of a probability distribution and of a network. However, in general a single fractal dimension does not suffice to quantify the…

### Thermodynamic and scaling behaviour in finite diffusion-limited aggregation

- Materials Science
- 1992

Renyi's entropies for diffusion-limited aggregates are studied as a function of the number N of particles contained in the aggregates. It is found that Renyi's values increase with log N in a linear…

### Comparative analysis of box-covering algorithms for fractal networks

- Computer ScienceAppl. Netw. Sci.
- 2021

This study aims to establish a unified framework for comparing approximating box-covering algorithms by collecting, implementing, and evaluating these methods in various aspects including running time and approximation ability.

### Estimating the Fractal Dimensions of Vascular Networks and Other Branching Structures: Some Words of Caution

- MathematicsMathematics
- 2022

Branching patterns are ubiquitous in nature, consequently over the years many researchers have tried to characterize the complexity of their structures. Due to their hierarchical nature and…

### FRACTAL ANALYSIS OF AGGREGATES OF NON-UNIFORMLY SIZED PARTICLES: AN APPLICATION TO MACAQUE MONKEY CORTICAL PYRAMIDAL NEURONS

- Biology
- 2001

Fractal dimension estimates obtained from the cumulative mass method are found to be useful for distinguishing two functionally different neuronal types which are visually similar.

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