Irregular Shapes: Randomness in Fractal Constructions

  • Heinz-Otto Peitgen
  • Hartmut Jürgens
  • Dietmar Saupe


Self-similarity seems to be one of the fundamental geometrical construction principles in nature. For millions of years evolution has shaped organisms based on the survival of the fittest. In many plants and also organs of animals, this has led to fractal branching structures. For example, in a tree the branching structure allows the capture of a maximum amount of sun light by the leaves; the blood vessel system in a lung is similarly branched so that a maximum amount of oxygen can be assimilated. Although the self-similarity in these objects is not strict, we can identify the building blocks of the structure — the branches at different levels.


Brownian Motion Fractal Dimension Random Forest Irregular Shape Percolation Threshold 
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Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Heinz-Otto Peitgen
    • 1
    • 2
  • Hartmut Jürgens
    • 1
  • Dietmar Saupe
    • 1
  1. 1.Institut für Dynamische SystemeUniversität BremenBremen 33Federal Republic of Germany
  2. 2.Department of MathematicsFlorida Atlantic UniversityBoca RatonUSA

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