# Multifractal phenomena in physics and chemistry

@article{Stanley1988MultifractalPI, title={Multifractal phenomena in physics and chemistry}, author={H. Stanley and P. Meakin}, journal={Nature}, year={1988}, volume={335}, pages={405-409} }

The neologism 'multifractal phenomena' describes the concept that different regions of an object have different fractal properties. Multifractal scaling provides a quantitative description of a broad range of heterogeneous phenomena.

#### 491 Citations

Phase-transition from fractality to homogeneity in a large-scale universe

- Physics
- 1996

Abstract Multifractal analysis of generalized luminosity fields gives evidence that the spatio-luminous distribution of galaxies in the observable universe has characteristic features of a phase… Expand

Fractals and Multifractals

- Mathematics
- 2010

To provide a brief introduction to fractals.
To introduce the notion of fractal dimension.
To provide a brief introduction to multifractals and define a multifractal formalism.
To… Expand

Multifractal Statistics of Mesoscopic Systems

- Mathematics
- 1999

A generalization of the Havlin–Bunde multifractal hypothesis is used to obtain a probability distribution corresponding to mesoscopic systems close to the critical regime. Good agreement between… Expand

Fractals in the Biological Sciences

- Mathematics
- 1996

The importance of spatial and temporal scaling to the study of biological systems and processes has long been recognized. We demonstrate that concepts derived from fractal and chaos theory are… Expand

Multifractals in diffusion and aggregation

- Mathematics
- 1990

The origin of the multifractal features which appear in several random systems is discussed. It is shown that for random fractals the multifractal features in the probability density of the diffusion… Expand

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… Expand

Multifractal scaling analysis of reactions over fractal surfaces

- Physics
- 1995

Abstract Simulations of the Eley-Rideal diffusion-limited reaction mechanism and its modified versions over surfaces of different fractal objects having different fractal dimensions were performed… Expand

Fractal Aspects of Galaxy Clustering

- Physics
- 1991

In the past decade, the mathematical concept of fractal has exerted a great influence in a large variety of scientific disciplines. It is very common to find recent papers on the application of… Expand

Calculation of multi-fractal dimensions in spin chains

- Physics, Medicine
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2014

Analytical derivations and numerical confirmations of the statement that the ground-state wave functions for a large variety of one-dimensional spin- models are multi-fractals in the natural spin-z basis are presented. Expand

A program for fractal and multifractal analysis of two-dimensional binary images: Computer algorithms versus mathematical theory

- Mathematics
- 2006

In this paper we present a tool to carry out the multifractal analysis of binary, two-dimensional images through the calculation of the Renyi D(q) dimensions and associated statistical regressions.… Expand

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