Japan Journal of Applied Mathematics

, Volume 1, Issue 1, pp 201–205 | Cite as

Physical models of fractal functions

  • Hideki Takayasu


By means of a simple model of electric resistance, physical meanings are given to the singular functions, de Wijs’ fractal, Lebesgue’s singular function and Takagi’s function.

Key words

fractal singular functions electric resistance shear flow 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    B. B. Mandelbrot, The Fractal Geometry of Nature. W. H. Freeman and Co., San Francisco, 1982.MATHGoogle Scholar
  2. [2]
    M. Hata and M. Yamaguti, The Takagi function and its generalization. Japan J. Appl. Math.,1 (1984), 183–199.MATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    B. B. Mandelbrot, Intermittent turbulence in self-similar cascade. J. Fluid Mech.,62 (1974), 331–358.MATHCrossRefGoogle Scholar
  4. [4]
    U. Frisch, P. L. Sulem and M. Nelkin, A simple dynamical model of intermittent fully developed turbulence. J. Fluid Mech.,87 (1978), 719–736.MATHCrossRefGoogle Scholar

Copyright information

© JJAM Publishing Committee 1984

Authors and Affiliations

  • Hideki Takayasu
    • 1
  1. 1.Department of PhysicsNagoya UniversityNagoyaJapan

Personalised recommendations