Multiaffinity and entropy spectrum of self-affine fractal profiles

Hiroaki Katsuragi, Haruo Honjo

    Research output: Contribution to journalArticle

    21 Citations (Scopus)

    Abstract

    The entropy spectrum method is applied to self-affine fractal profiles. First, the profile created by a generalized multiaffine generator is decomposed into many subsets having their own topological entropies. The entropy spectrum and [Formula Presented] (the [Formula Presented]th Hurst exponent) of its profile is calculated exactly. For each subset, [Formula Presented] (divider dimension) and [Formula Presented] (box dimension) are also calculated. The relation [Formula Presented] is obtained for the remaining subset after infinite iteration of the generator. Next, the entropy spectrum of fractional Brownian motion (FBM) traces is examined and obtained as a point spectrum. This implies that a variety of lengths of segments in FBM traces is caused not by intrinsic inhomogeneity or mixing of the Hurst exponents but by only the trivial fluctuation. Namely, there are no fluctuations in singularity or in topological entropy. Finally, a real mountain range (the Hida mountains in Japan) is also analyzed by this method. Despite the profile of the Hida mountains having two Hurst exponents, the entropy spectrum of its profile becomes a point spectrum again.

    Original languageEnglish
    Pages (from-to)254-262
    Number of pages9
    JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
    Volume59
    Issue number1
    DOIs
    Publication statusPublished - Jan 1 1999

    Fingerprint

    Self-affine
    Fractal
    fractals
    Hurst Exponent
    Entropy
    entropy
    profiles
    mountains
    Point Spectrum
    set theory
    Topological Entropy
    Fractional Brownian Motion
    exponents
    Subset
    Trace
    Generator
    Fluctuations
    Box Dimension
    generators
    Japan

    All Science Journal Classification (ASJC) codes

    • Statistical and Nonlinear Physics
    • Statistics and Probability
    • Condensed Matter Physics

    Cite this

    Multiaffinity and entropy spectrum of self-affine fractal profiles. / Katsuragi, Hiroaki; Honjo, Haruo.

    In: Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 59, No. 1, 01.01.1999, p. 254-262.

    Research output: Contribution to journalArticle

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