The metallic means family and multifractal spectra

✍ Scribed by Vera W. de Spinadel

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 363 KB
• Volume: 36
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/s0362-546x(98)00123-0

✦ Synopsis

Fractals are geometric or physical conÿgurations with self-similarity, that is, conÿgurations that remain invariant in the presence of "scale changes". Multifractals, are nontrivial structures that possess a spectrum of scaling indices, instead of the simple scaling structure shown in fractals. Usually, these non-regular fractal sets appear in physics, biology, chemistry, etc. Its characterization has been based on a multifractal spectral decomposition technique introduced by Procaccia [8].

The purpose of this paper is to show how, bridging between continued fractions expansions, generalized secondary Fibonacci sequences, hyperbolic geometry, Fuchsian groups and some members of the family of metallic means family, recently introduced by the author (see ), it is possible to state a mathematical model for the analysis of fractal and multifractal spectra.