• Tsuneyoshi Nakayama
  • Kousuke Yakubo
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 140)


In previous chapters we discussed geometrical properties of fractals characterized by fractal dimensions D f . However, the fractal dimension Df is not sufficient to describe all features of complex structures or distributions. For example, a distribution of mineral resources on earth is one such case. Gold is found in high densities only at a few rich places, whereas an extremely small amount of gold exists almost everywhere. Assume that areas with gold density larger than ρ1 are colored in red on a world atlas, and that areas with gold density larger than ρ2 (< ρ1) are colored in blue. Even if the distribution of red portions on the atlas is characterized by a fractal dimension D f , the fractal dimension of the blue region might differ from D f .It can be understood intuitively that the fractal dimension of the red region with very large ρ1 is close to zero, while the dimensionality of the blue region with very small ρ2 is almost two [4.1].


Fractal Dimension Voltage Drop Multifractal Spectrum Parabolic Approximation Growth Probability 
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© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Tsuneyoshi Nakayama
    • 1
  • Kousuke Yakubo
    • 1
  1. 1.Department of Applied Physics, Graduate School of EngineeringHokkaido UniversitySapporoJapan

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