Additive cellular automata and algebraic series
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.
scientific article; zbMATH DE number 440337
scientific article