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Analysis of Periodic and Intermediate Boundary 90/150 Cellular Automata
January 1996 (vol. 45 no. 1)
pp. 1-12

Abstract—Considerable interest has been recently generated in the study of Cellular Automata (CA) behavior. Polynomial and matrix algebraic tools are employed to characterize some of the properties of null/periodic boundary CA. Some other results of group CA behavior have been reported based on simulation studies. This paper reports a formal proof for the conjecture—there exists no primitive characteristic polynomial of 90/150 CA with periodic boundary condition. For generation of high quality pseudorandom patterns, it is necessary to employ CA having primitive characteristic polynomial. There exist two null boundary CA for every primitive polynomial. However, for such Cs the quality of pseudorandomness suffers in general, particularly in the regions around the terminal cells because of null boundary condition. In this background, a new concept of intermediate boundary CA has been proposed to generate pseudorandom patterns that are better in quality than those generated with null boundary CA. Some interesting properties of intermediate boundary CA are also reported.

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Index Terms:
Periodic boundary cellular automata, intermediate boundary cellular automata, matrix algebra, primitive polynomial, pseudorandom pattern.
S. Nandi, P.Pal Chaudhuri, "Analysis of Periodic and Intermediate Boundary 90/150 Cellular Automata," IEEE Transactions on Computers, vol. 45, no. 1, pp. 1-12, Jan. 1996, doi:10.1109/12.481481
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