Pascal’s Triangle : Cellular Automata and Attractors

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2004
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Peitgen, Heinz-Otto
Jürgens, Hartmut
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PEITGEN, Heinz-Otto, ed., Hartmut JÜRGENS, ed., Dietmar SAUPE, ed.. Chaos and Fractals : New Frontiers of Science. 2. ed.. New York: Springer, 2004, pp. 377-422. ISBN 978-0-387-20229-7. Available under: doi: 10.1007/0-387-21823-8_9
Zusammenfassung

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 Wolfram5 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.

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ISO 690PEITGEN, Heinz-Otto, Hartmut JÜRGENS, Dietmar SAUPE, 2004. Pascal’s Triangle : Cellular Automata and Attractors. In: PEITGEN, Heinz-Otto, ed., Hartmut JÜRGENS, ed., Dietmar SAUPE, ed.. Chaos and Fractals : New Frontiers of Science. 2. ed.. New York: Springer, 2004, pp. 377-422. ISBN 978-0-387-20229-7. Available under: doi: 10.1007/0-387-21823-8_9
BibTex
@incollection{Peitgen2004Pasca-42198,
  year={2004},
  doi={10.1007/0-387-21823-8_9},
  title={Pascal’s Triangle : Cellular Automata and Attractors},
  edition={2. ed.},
  isbn={978-0-387-20229-7},
  publisher={Springer},
  address={New York},
  booktitle={Chaos and Fractals : New Frontiers of Science},
  pages={377--422},
  editor={Peitgen, Heinz-Otto and Jürgens, Hartmut and Saupe, Dietmar},
  author={Peitgen, Heinz-Otto and Jürgens, Hartmut and Saupe, Dietmar}
}
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