Simplified model for fractal dimension of clouds

Physica A: Statistical Mechanics and its Applications

Abstract

Projections of three-dimensional random percolation clusters onto a two-dimensional plane give roughly the same fractal dimension 1.3 (for the perimeter versus area relation) as Lovejoy's observation of real clouds and cellular automata simulations of Nagel and Raschke.

Title:

Simplified model for fractal dimension of clouds

Authors:

Schneider, Marcus; Wöhlke, Thomas

Affiliation:

AA(Gesamtschule Castrop-Rauxel, W-4620 Castrop-Rauxel, Germany), AB(Gesamtschule Castrop-Rauxel, W-4620 Castrop-Rauxel, Germany)

Publication:

Physica A: Statistical Mechanics and its Applications, Volume 189, Issue 1, p. 1-3.

Publication Date:   

10/1992

Origin:

ELSEVIER

Abstract Copyright:

(c) 1992 Elsevier Science Publishers B.V. All rights reserved

DOI:

10.1016/0378-4371(92)90121-6

Bibliographic Code:

1992PhyA..189....1S

Citations

Tahavvor, A.R., Zakeri, E., Moezi, S.A.
Modeling of frost growth on a horizontal circular cylinder under natural convection using fractal geometry analysis  
Iranian Journal of Science and Technology - Transactions of Mechanical Engineering, 2014


Gouravaraju S., Ganguli R.
Estimating the Hausdorff-Besicovitch dimension of boundary of basin of attraction in helicopter trim
Applied Mathematics and Computation, Volume 218, 2012


Shih, A.-Z.
An examination of fractal dimension approach of image classification  
Proceedings of the 7th International Conference on Machine Learning and Cybernetics, ICMLC, 2008


Ivanova K., Ausloos M., Davis A.B., Ackerman T.P.

Atmospheric data analysis with the i-variability diagram method: Hint to fractional Brownian motion-like phenomena for the inner structure of clouds

Physica A: Statistical Mechanics and its Applications, Volume 272, 1999


Bershadskii A.
Large-scale percolation and diffusion in turbulent stratosphere
Physica A: Statistical Mechanics and its Applications, Volume 206, 1994


 

References

Lovejoy, S.
Area-Perimeter Relation for Rain and Cloud Areas
Science, Volume 216, Issue 4542, pp. 185-187, 1982


Nagel, K.; Raschke, E.
Self-organizing criticality in cloud formation?
Physica A: Statistical Mechanics and its Applications, Volume 182, Issue 4, p. 519-531, 1992


A Margolina,Michel Rosso
Illumination: A new method for studying 3D percolation fronts in a concentration gradient
Journal of Physics A: Mathematical and General, Volume 25, Number 14, 1992


P Grassberger
Numerical studies of critical percolation in three dimensions
Journal of Physics A: Mathematical and General, Volume 25, Number 22, 1992


Dietrich Stauffer,A. Aharony
Percolation Theory: An Introduction
Taylor and Francis, London, 1994


P. L. Leath
Cluster size and boundary distribution near percolation threshold
Phys. Rev. B 14, 5046, 1976


 

Further Readings


Dietrich Stauffer:
From Newton to Mandelbrot: A Primer in Theoretical Physics
Springer-Verlag; 1st ed. 1990. Corr. 2nd printing edition (1 Jan. 1990)


Benoit B. Mandelbrot
The Fractal Geometry of Nature
Henry Holt and Company, 1982


 

The fractal Geometry of Nature

Benoit B Mandebrot