Recursive Structures: Growing of Fractals and Plants

  • Heinz-Otto Peitgen
  • Hartmut Jürgens
  • Dietmar Saupe


The historical constructions of fractals by Cantor, Sierpinski, von Koch, Peano, etc., have been labeled as ‘mathematical monsters’. Their purpose had been mainly to provide certain counterexamples, for example, showing that there are curves that go through all points in a square. Today a different point of view has emerged due to the ground-breaking achievements of Mandelbrot. Those strange creations from the turn of the century are anything but exceptional counterexamples; their features are in fact typical of nature. Consequently, fractals are becoming essential components in the modeling and simulation of nature. Certainly, there is a great difference between the basic fractals shown in this book and their counterparts in nature: mountains, rivers, trees, etc. Surely, the artificial fractal mountains produced today in computer graphics already look stunningly real. But on the other hand they still lack something we would certainly feel while actually camping in the real mountains. Maybe it is the (intentional) disregarding of all developmental processes in the fractal models which is one of the factors responsible for this shortcoming.


Line Segment Production Rule Initial Image Graphical Interpretation Recursive Structure 
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Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Heinz-Otto Peitgen
    • 1
    • 2
  • Hartmut Jürgens
    • 3
  • Dietmar Saupe
    • 4
  1. 1.CeVis and MeVisUniversität BremenBremenGermany
  2. 2.Department of MathematicsFlorida Atlantic UniversityBoca RatonUSA
  3. 3.CeVis and MeVisUniversität BremenBremenGermany
  4. 4.Department of Computer ScienceUniversität FreiburgFreiburgGermany

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