Limited Selfsimilarity

  • H. R. Bittner
Conference paper
Part of the Beiträge zur Graphischen Datenverarbeitung book series (GRAPHISCHEN)

Abstract

Measuring natural objects with biggest and smallest details at varied resolutions leads to fractal properties within certain limits. Thus selfsimilarity can be found only asymptotically in a confined range of scale. If the description is restricted to the selfsimilar range only, which may be far from the limits, the influence of all values outside this range, which can be measured with similar precision, is neglected. Depending on the actual task, this effect could be negligible, or considerable. In order to include the topological and the intermittent range for the description of architecture with small and medium range of selfsimilarity as well, the use of a log-logistic fitting function is proposed, taking into account also a fractal or topological scaling residue.

Keywords

Porosity Glycerol Filtration Topo 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [BAC91]
    P. Bach: Mikrointerferometrische Bestimmung der Porenvolumenverteilung von Cornea und Kontaktlinse und ihre fraktale Interpretation. Thesis, Gießen 1991Google Scholar
  2. [BIT89]
    H.R. Bittner, P. Wlczek, M. Sernetz: Characterization of Fractal Biological Objects by Image Analysis. Acta Stereologica, 1989, 8, 31–40Google Scholar
  3. [BIT91a]
    H.R. Bittner, M. Sernetz: Selfsimilarity within Limits — Description with the Log-Logistic Function. In: H.-O. Peitgen, J.M. Henriques and L.F. Penedo (Eds.): FRACTAL′90 — Proc. of the 1st IF1P Conference on Fractals. Lisbon, June 6–8, 1990, Elsevier, Amsterdam 1991 (in press)Google Scholar
  4. [BIT91b]
    H.R. Bittner: Modelling of Fractal Vessel Systems. In: FRACTAL′90 (see above), 1991Google Scholar
  5. [MAN82]
    B.B. Mandelbrot: Fractal Geometry of Nature, Freeman, New York, 1982MATHGoogle Scholar
  6. [SER89]
    M. Sernetz, H.R. Bittner, H. Willems, C. Baumhoer: Chromatography. In: D. Avnir (Ed.): The Fractal Approach to Heterogeneous Chemistry. J. Wiley, 1989, 361–379Google Scholar
  7. [SER90]
    M. Sernetz, H. Willems, H.R. Bittner; Fractal Organization of Metabolism. In: W. Wieser, E. Gnaiger (Eds.): Energy Transformations in Cells and Organisms. Thieme, Stuttgart 1990, 82–90Google Scholar
  8. [SER91]
    M. Sernetz, H.R. Bittner, P. Bach, B. Glittenberg: Fractal Characterization of the Porosity of Organic Tissue by Interferometry. In.: F. Rodriguez-Reinoso, K.S.W. Sing, J. Rouquerol (Eds.): Characterization of Porous Solids II (COPS II, Alicante, May, 1990), Elsevier, Amsterdam 1991,141–150Google Scholar
  9. [TÉL88]
    T. Tél: Fractals, Multifractals, and Thermodynamics, Z. Naturforschung 43a, 1988, 1154–1174Google Scholar
  10. [WES86]
    B.J. West, V. Bhargava, A. Goldberger: Beyond the Principle of Similitude: Renormalization in the Bronchial Tree. J. Applied Physiology 60(3), 1986, 1089–1097Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • H. R. Bittner
    • 1
  1. 1.Institut für Biochemie und EndokrinologieGießenGermany

Personalised recommendations