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


Fractal structures are classified into two categories, i.e., deterministic fractals and random fractals. Deterministic fractal structures can be easily understood by presenting some examples. A typical example is the Mandelbrot—Given fractal [2.1], which can be constructed by starting with a structure with 8 line segments as shown in Fig. 2.1 a (the first stage of the Mandelbrot—Given fractal). In the second stage, each line segment of the initial structure is replaced by the initial structure itself (Fig. 2.2b). This process is repeated indefinitely. The Mandelbrot—Given fractal possesses an obvious dilatational symmetry, as seen from Fig. 2.1c, i.e., if we magnify a part of the structure, the enlarged portion looks just like the original one.


Brownian Motion Fractal Dimension Line Segment Initial Structure Hausdorff Dimension 
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Copyright information

© 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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