Topic
Fractal dimension
About: Fractal dimension is a research topic. Over the lifetime, 14764 publications have been published within this topic receiving 329050 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this article, it was shown that fractals in general and strange attractors in particular are characterized by an infinite number of generalized dimensions Dq, q > 0, which correspond to exponents associated with ternary, quaternary and higher correlation functions.
1,577 citations
Book•
01 Jan 1997
TL;DR: A review of fractal geometry can be found in this article, with a focus on the Ergodic Theorem and Fractals, as well as the renewalal theorem and fractals.
Abstract: Mathematical Background. Review of Fractal Geometry. Some Techniques for Studying Dimension. Cookie-cutters and Bounded Distortion. The Thermodynamic Formalism. The Ergodic Theorem and Fractals. The Renewal Theorem and Fractals. Martingales and Fractals. Tangent Measures. Dimensions of Measures. Some Multifractal Analysis. Fractals and Differential Equations. References. Index.
1,553 citations
TL;DR: In this article, the authors showed that fractal surfaces can be super water repellent (superwettable) when the surfaces are composed of hydrophobic (hydrophilic) materials.
Abstract: Wettability of fractal surfaces has been studied both theoretically and experimentally. The contact angle of a liquid droplet placed on a fractal surface is expressed as a function of the fractal dimension, the range of fractal behavior, and the contacting ratio of the surface. The result shows that fractal surfaces can be super water repellent (superwettable) when the surfaces are composed of hydrophobic (hydrophilic) materials. We also demonstrate a super-water-repellent fractal surface made of alkylketene dimer; a water droplet on this surface has a contact angle as large as 174°.
1,500 citations
TL;DR: In this paper, the authors developed three indices of pattern derived from information theory and fractal geometry for 94 quadrangles covering most of the eastern United States using digitized maps.
Abstract: Landscape ecology deals with the patterning of ecosystems in space. Methods are needed to quantify aspects of spatial pattern that can be correlated with ecological processes. The present paper develops three indices of pattern derived from information theory and fractal geometry. Using digitized maps, the indices are calculated for 94 quadrangles covering most of the eastern United States. The indices are shown to be reasonably independent of each other and to capture major features of landscape pattern. One of the indices, the fractal dimension, is shown to be correlated with the degree of human manipulation of the landscape.
1,453 citations
01 Jan 1997
TL;DR: Panagiotopoulos, O.K.Carpinteri, B. Chiaia, R. Gorenflo, F. Mainardi, and R. Lenormand as mentioned in this paper.
Abstract: A. Carpinteri: Self-Similarity and Fractality in Microcrack Coalescence and Solid Rupture.- B. Chiaia: Experimental Determination of the Fractal Dimension of Microcrack Patterns and Fracture Surfaces.- P.D. Panagiotopoulos, O.K. Panagouli: Fractal Geometry in Contact Mechanics and Numerical Applications.- R. Lenormand: Fractals and Porous Media: from Pore to Geological Scales.- R. Gorenflo, F. Mainardi: Fractional Calculus: Integral and Differential Equations of Fractional Order.- R. Gorenflo: Fractional Calculus: some Numerical Methods.- F. Mainardi: Fractional Calculus: some Basic Problems in Continuum and Statistical Mechanics.
1,389 citations