Abstract
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).
Keywords
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D.-U. Hwang, Complex networks: structure and dynamics. Phys. Rep. 424(4–5), 175–308 (2006)
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)
W. Feller, An Introduction to Probability Theory and Its Applications I (Wiley, New York, 1950)
J. Kari, Representation of reversible cellular automata with block permutation. Math. Syst. Theory 29(1), 47–61 (1996)
K. Mainzer, The Little Book of Time (Copernicus Books, New York, 2002)
K. Morita, M. Harao, Computation universality of one-dimensional reversible (injective) cellular automata. Trans. IEICE E 72, 758–762 (1989)
R.G. Sachs, The Physics of Time Reversal (University of Chicago, Chicago, 1987)
T. Toffoli, Computation and construction universality of reversible cellular automata. J. Comput. Syst. Sci. 15, 213–231 (1977)
S. Wolfram, A New Kind of Science (Wolfram Media, Champaign Il, 2002)
H.-D. Zeh, The Physical Basis of the Direction of Time, 5th edn. (Berlin, Springer, 2007)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2012 Klaus Mainzer
About this chapter
Cite this chapter
Mainzer, K., Chua, L. (2012). Time in the Universe of Cellular Automata. In: The Universe as Automaton. SpringerBriefs in Complexity. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23477-4_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-23477-4_6
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23476-7
Online ISBN: 978-3-642-23477-4
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)