An examination of Figures (10–14) at the end of the last chapter shows that, except for period-k isle of Eden bit strings (Figs. 12, 14b), all attractors of the cellular automaton 62 have a non-empty basin of attraction with several gardens of Eden. Therefore, given any bit string on an attractor, it is impossible to retrace its dynamics in backward time to find where it had originated in the transient regime. Unlike in ordinary differential equations used in modeling dynamical systems, it is impossible, for most rules of cellular automata, to retrace its past history on the attractor. This observation leads us to exciting and deep insights in the concept of time with respect to the universe of cellular automata and physics (Chua et al. 2006; Mainzer 2002; Sachs 1987).
Cellular Automaton Modeling Dynamical System Local Rule Transient Regime Attractor Representation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.
L.O. Chua, V.I. Sbitnev, S. Yoon, A nonlinear dynamics perspective of Wolfram’s new kind of science Part VI: from time-reversible attractors to the arrow of time. Int. J. Bifurcat. Chaos (IJBC) 16(5), 1097–1373 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
W. Feller, An Introduction to Probability Theory and Its Applications I (Wiley, New York, 1950)zbMATHGoogle Scholar