1991
//
Surfaces/Materials

Multifractality of self-affine fractals

Abstract
The concept of multifractality is extended to self-affine fractals in order to provide a more complete description of fractal surfaces. We show that for a class of iteratively constructed self-affine functions there exists an infinite hierarchy of exponents Hq describing the scaling of the qth order height-height correlationfunction Cq(x)~xqhq. Possible applications to random walks and turbulent flows are discussed. It is demonstratedon on the example of random walks along a chain that for stochastic lattice models leading to self-affine fractals Hq exhibits phase-transition-like behavior.

..

More publications
L.A.N. Amaral, A.-L. Barabási, S.V. Buldyrev, S.T. Harrington, S. Havlin, R. Sadr-Lahijani, H.E. Stanley

Physical Review E 51, 4655–4673 (1995)

view
P. Jensen, A.-L. Barabási, H. Larralde, S. Havlin, H.E. Stanley

Nature 368, 22 (1994)

view
A.-L. Barabási, R. Bourbonnais, M. Jensen, J. Kertesz, T. Vicsek, Y.-C. Zhang

Physical Review A 45, R6951–R6954 (1992)

view