Pascal’s Triangle: Cellular Automata and Attractors
Being introduced to the Pascal triangle for the first time, one might think that this mathematical object is 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 of Fractals for the Classroom, Part One we introduced one example: the relation between the Pascal triangle and the Sierpinski gasket.
KeywordsCellular Automaton Binomial Coefficient Sierpinski Gasket Divisibility Property Pascal Triangle
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