Complex Systems

Period Multiplying Operators on Integer Sequences Modulo A Prime Download PDF

Burton Voorhees
Athabasca University, Box 10,000,
Athabasca, Alberta TOG 2RO, Canada


We study properties of operators defined on the space of right half-infinite sequences with entries chosen from where is prime. The operators in question allow solution of the problem of finding predecessor states for certain cellular automata evolutions and they can be thought of as discrete integration with respect to sequence index.

These operators are self-accumulating, not solipsistic, and have no dense orbits. In addition, they exhibit a period-multiplying property. Many of these results are derived from properties of Pascal's triangle modulo which are presented in an appendix.