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The Universe as Automaton

Part of the SpringerBriefs in Complexity Book Series

DOI: 10.1007/978-3-642-23477-4

ISBN: 978-3-642-23476-7

Publisher: Springer Berlin Heidelberg - Springer Journals

Sep 30, 2011

1 - 9 of 9 Chapters

LitStream

Chapter 1Introduction: Leibniz, Turing, Zuse, and Beyond

Mainzer, Klaus; Chua, Leon

Pages: 1 –16

[According to Einstein, a scientific explanation should be as simple as possible, but not too simple, for it to be realistic. It would be nice to understand the great scientific problems of the universe (such as cosmic expansion, black holes, the evolution of life, and brains) with just basic...
LitStream

Chapter 2Simplicity in the Universe of Cellular Automata

Mainzer, Klaus; Chua, Leon

Pages: 17 –24

[Because of their simplicity, rules of cellular automata can easily be understood. In a very simple version, we consider two-state one-dimensional cellular automata (CA) made of identical cells with a periodic boundary condition. In this case, the object of study is a ring of coupled cells with L...
LitStream

Chapter 3Complexity in the Universe of Cellular Automata

Mainzer, Klaus; Chua, Leon

Pages: 25 –30

[The colored toy cubes contain all the information about the complex dynamics of cellular automata. An important advantage of the Boolean cube representation is that it allows us to define an index of complexity (Chua et al. 2002). Each one of the 256 cubes is obviously characterized by different...
LitStream

Chapter 4Symmetry in the Universe of Cellular Automata

Mainzer, Klaus; Chua, Leon

Pages: 31 –43

[A cursory inspection of the discrete time evolutions of the 256 local rules reveals some similarity and partial symmetry among various evolved patterns. It reminds us of more-or-less random observations in the natural sciences that demand the unification of mathematical explanations with...
LitStream

Chapter 5Attractors in the Universe of Cellular Automata

Mainzer, Klaus; Chua, Leon

Pages: 45 –65

[One-dimensional cellular automata with L = I + 1 cells are complex systems with nonlinear dynamics determined by one of the 256 local rules N.]
LitStream

Chapter 6Time in the Universe of Cellular Automata

Mainzer, Klaus; Chua, Leon

Pages: 67 –74

[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...
LitStream

Chapter 7Matter in the Universe of Cellular Automata

Mainzer, Klaus; Chua, Leon

Pages: 75 –85

[In the universe of cellular automata, one can identify many concrete concepts and examples that mimic concepts and phenomena of matter in the classical, quantum, and relativistic world of physics. Historically, quantum theory started with Bohr’s atomic model of an atomic nucleus and discrete...
LitStream

Chapter 8Life and Brain in the Universe of Cellular Automata

Mainzer, Klaus; Chua, Leon

Pages: 87 –103

[Historically, in science and philosophy people believed in a sharp difference between “dead” and “living” matter. Aristotle interpreted life as the power of self-organization (entelechy) driving the growth of plants and animals to their final form. A living system is able to reproduce itself and...
LitStream

Chapter 9Outlook: Is the Universe a Computer?

Mainzer, Klaus; Chua, Leon

Pages: 105 –108

[ To answer this question, a deeper analysis of our cosmological models is necessary. In general, principles of symmetry play a central role in physics. The invariance and covariance properties of a system under specific symmetry transformations can either be related to the conservation laws of...

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