Multifractality of self-affine fractals

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.


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

Physical Review A 45, R6951–R6954 (1992)

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

Fractals 4, 307–319 (1996)

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

Fractals 4, 321–329 (1996)