Library

feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Pure and applied geophysics 131 (1989), S. 5-42 
    ISSN: 1420-9136
    Keywords: Fractal ; multifractal ; measure ; Hölder ; limit theorem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract This text is addressed to both the beginner and the seasoned professional, geology being used as the main but not the sole illustration. The goal is to present an alternative approach to multifractals, extending and streamlining the original approach inMandelbrot (1974). The generalization from fractalsets to multifractalmeasures involves the passage from geometric objects that are characterized primarily by one number, namely a fractal dimension, to geometric objects that are characterized primarily by a function. The best is to choose the function ϱ(α), which is a limit probability distribution that has been plotted suitably, on double logarithmic scales. The quantity α is called Hölder exponent. In terms of the alternative functionf(α) used in the approach of Frisch-Parisi and of Halseyet al., one has ϱ(α)=f(α)−E for measures supported by the Euclidean space of dimensionE. Whenf(α)≥0,f(α) is a fractal dimension. However, one may havef(α)〈0, in which case α is called “latent.” One may even have α〈0, in which case α is called “virtual.” These anomalies' implications are explored, and experiments are suggested. Of central concern in this paper is the study of low-dimensional cuts through high-dimensional multifractals. This introduces a quantityD q, which is shown forq〉1 to be a critical dimension for the cuts. An “enhanced multifractal diagram” is drawn, includingf(α), a function called τ(q) andD q.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...