Pascal’s Triangle: Cellular Automata and Attractors

  • Heinz-Otto Peitgen
  • Hartmut Jürgens
  • Dietmar Saupe

Abstract

Being introduced to the Pascal triangle for the first time, one might think that this mathematical object was a rather innocent one. Surprisingly it has attracted the attention of innumerable scientists and amateur scientists over many centuries. One of the earliest mentions (long before Pascal’s name became associated with it) is in a Chinese document from around 1303.1 Boris A. Bondarenko,2 in his beautiful recently published book, counts several hundred publications which have been devoted to the Pascal triangle and related problems just over the last two hundred years. Prominent mathematicians as well as popular science writers such as Ian Stewart,3 Evgeni B. Dynkin and Wladimir A. Uspenski,4 and Stephen Wolframs have devoted articles to the marvelous relationship between elementary number theory and the geometrical patterns found in the Pascal triangle. In chapter 2 we introduced one example: the relation between the Pascal triangle and the Sierpinski gasket.

Keywords

Cellular Automaton Iterate Function System Binomial Coefficient Sierpinski Gasket Black Cell 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Reference

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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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