Multifractality of self-affine fractals

Albert Lszl Barabsi, Tams Vicsek

Research output: Contribution to journalArticle

298 Citations (Scopus)


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 correlation function cq(x)xqqH. Possible applications to random walks and turbulent flows are discussed. It is demonstrated 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.

Original languageEnglish
Pages (from-to)2730-2733
Number of pages4
JournalPhysical Review A
Issue number4
Publication statusPublished - Jan 1 1991

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

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