Multifractality of self-affine fractals

Albert Lszl Barabsi*, Tams Vicsek

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract (may include machine translation)

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
Volume44
Issue number4
DOIs
StatePublished - 1991
Externally publishedYes

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