Additive cellular automata and algebraic series (Q688164)
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scientific article; zbMATH DE number 440337
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Additive cellular automata and algebraic series |
scientific article; zbMATH DE number 440337 |
Statements
Additive cellular automata and algebraic series (English)
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1 December 1993
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A class of one-dimensional cellular automata in which the value of each cell depends in additive manner of its neighbours is studied. Generating series are used to describe the behavior of a cell in time and their basic properties are proved. Also it is shown that proper generating functions can be computed directly in the cases where the values of a cell are elements of a finite field or are complex numbers. In the second part of the paper a number of examples is given relating additive cellular automata and some ``automatic sequences'' like paper folding sequences, or Catalan or Motzkin numbers.
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algebraic series
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Catalan numbers
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automatic sequences
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cellular automata
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generating functions
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paper folding sequences
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Motzkin numbers
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