Abstract
It is demonstrated that clusters constructed by asymmetric recursion rules can be described in terms of mass multifractality. The set of generalized dimensions D q associated with the geometry of such objects is determined numerically for the growing asymmetric Cantor set using the box counting and the sand box methods. These approaches are not found equally efficient in evaluating the D q values. The direct determination of the f(α) spectrum corresponding to the singular distribution of mass in very large off-lattice diffusion-limited aggregates indicates the mass multifractality of these clusters as well.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Mandelbrot, B. B., 1982 The Fractal Geometry of Nature ( Freeman, San Francisco )
H. Takayasu, Fractals in Physical Sciences ( Asakura Shoten Publishers, Tokio, 1985 ) (in Japanese)
J. Feder Fractals ( Plenum Press, New York, 1988 )
T. Vicsek Fractal Growth Phenomena (World Scientific, Singapore, 1989 jan.)
R. M. Brady and R. C. Ball, Nature 309, 225 (1984)
M. Matsushita, M. Sano, Y. Hayakawa, H. Honjo and Y. Sawada, Phys. Rev. Lett. 53, 286 (1984)
H. Honjo, S. Ohta and M. Matsushita, J. Phys. Soc. Japan 55, 2487 (1986)
Gy. Radnoczy, T. Vicsek, L. M. Sander and D. Grier, Phys. Rev. A35, 4012 (1987)
L. Niemeyer, L. Pietronero and H. J. Wiesmann, Phys. Rev. Lett. 52, 1033 (1984)
Daccord, G., Nittmann, J., and Stanley, H. E., 1986 Phys.Rev. Lett. 56, 336
Maloy, K. J., Feder J. and Jossang, J., 1985 Phys. Rev. Lett. 55, 2681
H. Herrmann, Phys. Rep. 136, 154 (1986)
P. Meakin, in Phase Transitions and Critical Phenomena edited by C. Domb and J. L. Lebowitz, Vol. 12, ( Academic Press, New York, 1987 ) p. 365
Stanley, H. E. and Ostrowsky, N., editors, Random Fluctuations and Pattern Growth ( Kluwer, Dordrecht, 1988 )
R. Jullien and R. Botet Aggregation and Fractal Aggregates ( World Scientific, Singapore, 1987 )
T. C. Halsey, P. Meakin and I. Procaccia, Phys. Rev. Lett. 56, 854 (1986)
C. Amitrano, A. Coniglio and F. di Liberto, Phys. Rev. Lett. 57, 1016 (1986)
Y. Hayakawa, S. Sato and M. Matsushita, Phys. Rev. A36, 1963 (1987)
J. Nittmann, H. E. Stanley, E. Torboul and G. Daccord, Phys. Rev. Lett. 58, 619 (1987)
S. Ohta and H. Honjo, Phys. Rev. Lett. 60, 611 (1988)
B. B. Mandelbrot, J. Fluid. Mech 62, 331 (1974)
U. Frisch and G. Parisi, in Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics edited by M. Ghil, R. Benzi and G. Parisi (North- Holland, Amsterdam, 1985 )
T. C. Halsey, M. H. Jensen, L. P. Kadanoff, I. Procaccia and B. Shraiman, Phys. Rev. A33, 1141 (1986)
T. Tél, Z. Naturforsch, 43a, 1154, 1988
B. B. Mandelbrot in Random Fluctuations and Pattern Growth edited by H. E. Stanley and N. Ostrowsky ( Kluwer, Dordrecht, 1988 ) p. 333
T. A. Witten and L. M. Sander, Phys. Rev. Lett 47, 1400 (1981)
F. Argoul, A. Arneodo, G. Grasseau and H. L. Swinney, Phys. Rev. Lett. 61, 2558 (1988)
T. Nagatani, preprint
J. P. Hansen, J. L. McCauley, J. Muller and A. Skjeltorp, in Random Fluctuations and Pattern Growth edited by H. E. Stanley and N. Ostrowsky ( Kluwer, Dordrecht, 1988 ) p. 369
P. Meakin, private communication
T. Tél and T. Vicsek, J. Phys. A20, L835 (1987)
T. Vicsek, J. Phys. A16, L647 (1983)
I. Procaccia and R. Zeitak, Phys. Rev. Lett. 60, 2511 (1988)
P. Garik, R. Richter, J. Hautman and P. Ramanlal, Phys. Rev. A32, 3156 (1985)
F. Family, D. Piatt and T. Vicsek, J. Phys. A20, L1177 (1987)
T. Tél, A. Fülöp and T. Vicsek, preprint
A. Chhabra and R. V. Jensen, preprint
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Vicsek, T. (1990). Mass Multifractality in Cluster Growth Models. In: Landau, D.P., Mon, K.K., Schüttler, HB. (eds) Computer Simulation Studies in Condensed Matter Physics II. Springer Proceedings in Physics, vol 45. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-75234-6_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-75234-6_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-75236-0
Online ISBN: 978-3-642-75234-6
eBook Packages: Springer Book Archive