Journal
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Volume 24, Issue 9, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218127414501168
Keywords
Cellular automata with memory; Lempel-Ziv complexity; spectral analysis; phase transition
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We study elementary cellular automata with memory. The memory is a weighted function averaged over cell states in a time interval, with a varying factor which determines how strongly a cell's previous states contribute to the cell's present state. We classify selected cell-state transition functions based on Lempel-Ziv compressibility of space-time automaton configurations generated by these functions and the spectral analysis of their transitory behavior. We focus on rules 18, 22, and 54 because they exhibit the most intriguing behavior, including computational universality. We show that a complex behavior is observed near the nonmonotonous transition to null behavior (rules 18 and 54) or during the monotonic transition from chaotic to periodic behavior (rule 22).
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