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A nonlinear dynamics perspective of Wolfram's new kind of science. Volume III /
Volume III continues the author's quest for developing a pedagogical, self-contained, yet rigorous analytical theory of 1-D cellular automata via a nonlinear dynamics perspective. Using carefully conceived and illuminating color graphics, the global dynamical behaviors of the 50 (out of 256) lo...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore ; Hackensack, N.J. :
World Scientific Pub. Co.,
©2009.
|
| Colección: | World Scientific series on nonlinear science. Monographs and treatises ;
v. 68. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Chua, Leon O., |d 1936- |1 https://id.oclc.org/worldcat/entity/E39PBJrRbHY6ykbmyVgHqWkJjC | |
| 245 | 1 | 2 | |a A nonlinear dynamics perspective of Wolfram's new kind of science. |n Volume III / |c Leon O. Chua. |
| 246 | 3 | |a Volume 3 | |
| 246 | 3 | |a Volume three | |
| 260 | |a Singapore ; |a Hackensack, N.J. : |b World Scientific Pub. Co., |c ©2009. | ||
| 300 | |a 1 online resource (xv, 340 pages) : |b color illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 380 | |a Bibliography | ||
| 490 | 1 | |a World Scientific series on nonlinear science. Series A, Monographs and treatises ; |v v. 68 | |
| 504 | |a Includes bibliographical references (page 331) and index. | ||
| 505 | 0 | |a ch. 1. Isles of Eden. 1. Recap of main results from parts I to VI. 1.1. Local rules and Boolean cubes. 1.2. Threshold of complexity. 1.3. Only 88 local rules are independent. 1.4. Robust characterization of 70 independent local rules. 2. Basin tree diagrams of ten complex Bernoulli shift rules. 2.1. Basin of attraction and basin trees. 2.2. Garden of Eden. 2.3. Isle of Eden. 2.4. Gallery of basin tree diagrams. 3. Global analysis of local rule 90. 3.1. Ru1e 90 has no Isle of Eden. 3.2. Period of Rule 90 grows with L. 3.3. Global state-transition formula for rule 90. 3.4. Periodicity constraints of rule 90. 4. Global analysis of local rules 150 and 105. 4.1. Rules 150 and 105 are composed of Isles of Eden if L is not divisible by 3. 4.2. Global state-transition formula for rules 150 and 105. 4.3. Rules 150 and 105 are globally quasi-equivalent. 5. Concluding remarks -- ch. 2. More Isles of Eden. 1. The beginning of the end. 2. Basin tree diagrams of eight hyper Bernoulli shift rules. 2.1. Highlights from rule 26. 2.2. Highlights from rule 30. 2.3. Highlights from rule 41. 2.4. Highlights from rule 45. 2.5. Highlights from rule 60. 2.6. Highlights from rule 106. 2.7. Highlights from rule 110. 2.8. Highlights from rule 154. 3. Global analysis of local rule 60. 3.1. Rule 60 has no Isles of Eden. 3.2. Period of rule 60 grows with L. 3.3. Global state-transition formula for rule 60. 3.4. Periodicity constraints of rule 60. 4. Global analysis of local rule 154 and 45. 5. Dense Isles-of-Eden property. 5.1. Notations and definitions. 5.2. Four basic lemmas. 5.3. Locating points with multiple preimages. 5.4. Constructing the Isles of Eden digraph. 5.5. The full Isles of Eden digraph. 5.6. Nondegenerate cycles and Isles of Eden. 5.7. Effect of global equivalence transformations on Isles of Eden digraphs. 5.8. Dense Isles of Eden from rule 45 and rule 154. 5.9. Dense Isles of Eden from rule 105 and rule 150. 5.10. Gallery of Isles of Eden digraphs of eight representative local rules. 6. Concluding remarks. | |
| 520 | |a Volume III continues the author's quest for developing a pedagogical, self-contained, yet rigorous analytical theory of 1-D cellular automata via a nonlinear dynamics perspective. Using carefully conceived and illuminating color graphics, the global dynamical behaviors of the 50 (out of 256) local rules that have not yet been covered in Volumes I and II are exposed via their stunningly revealing basin tree diagrams. The Bernoulli??-shift dynamics discovered in Volume II is generalized to hold for all 50 (or 18 globally equivalent) local rules via complex and hyper Bernoulli wave dynamics. Explicit global state transition formulas derived for rules 60, 90, 105, and 150 reveal a new scale-free phenomenon. The most surprising new result unveiled in this volume is the "Isle of Eden" found hidden in most (almost 90%) of the 256 local rules. Readers are challenged to hunt for long-period, isolated Isles of Eden. These are rare gems waiting to be discovered | ||
| 588 | 0 | |a Print version record. | |
| 506 | |3 Use copy. |5 MiAaHDL | ||
| 538 | |a Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. |u http://purl.oclc.org/DLF/benchrepro0212 |5 MiAaHDL | ||
| 546 | |a English. | ||
| 583 | 1 | |a digitized |c 2011 |h HathiTrust Digital Library |l committed to preserve |2 pda |5 MiAaHDL | |
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 600 | 1 | 0 | |a Wolfram, Stephen. |t New kind of science. |
| 630 | 0 | 7 | |a New kind of science (Wolfram, Stephen) |2 fast |
| 650 | 0 | |a Cellular automata. | |
| 650 | 0 | |a Computational complexity. | |
| 650 | 0 | |a Dynamics. | |
| 650 | 0 | |a Nonlinear theories. | |
| 650 | 4 | |a Cellular automata. | |
| 650 | 4 | |a Computational complexity. | |
| 650 | 4 | |a Dynamics. | |
| 650 | 4 | |a Nonlinear theories. | |
| 650 | 4 | |a Wolfram, Stephen. |x New kind of science. | |
| 650 | 4 | |a Mathematics. | |
| 650 | 4 | |a Physical Sciences & Mathematics. | |
| 650 | 4 | |a Algebra. | |
| 650 | 6 | |a Automates cellulaires. | |
| 650 | 6 | |a Complexité de calcul (Informatique) | |
| 650 | 6 | |a Dynamique. | |
| 650 | 6 | |a Théories non linéaires. | |
| 650 | 7 | |a kinetics (dynamics) |2 aat | |
| 650 | 7 | |a COMPUTERS |x Machine Theory. |2 bisacsh | |
| 650 | 7 | |a Cellular automata |2 fast | |
| 650 | 7 | |a Computational complexity |2 fast | |
| 650 | 7 | |a Dynamics |2 fast | |
| 650 | 7 | |a Nonlinear theories |2 fast | |
| 710 | 2 | |a World Scientific (Firm) | |
| 776 | 1 | |z 9812837930 | |
| 776 | 1 | |z 9789812837936 | |
| 830 | 0 | |a World Scientific series on nonlinear science. |n Series A, |p Monographs and treatises ; |v v. 68. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=1679749 |z Texto completo |
| 880 | 0 | |6 505-00/(S |a CONTENTS; Volume III; Chapter 1. Isles of Eden; 1. Recap of Main Results from Parts I to VI; 1.1. Local rules and Boolean cubes; 1.2. Threshold of complexity; 1.3. Only 88 local rules are independent; 1.4. Robust characterization of 70 independent local rules; 1.4.1. Steady-state behavior 1: Period-1 attractors or period-1 isles of Eden; 1.4.2. Steady-state behavior 2: Period-2 attractors or period-2 isles of Eden; 1.4.3. Steady-state behavior 3: Period-3 attractors; 1.4.4. Steady-state behavior 4: Bernoulli στ -shift attractors or isles of Eden. | |
| 880 | |6 520-00/(S |a Volume III continues the author's quest for developing a pedagogical, self-contained, yet rigorous analytical theory of 1-D cellular automata via a nonlinear dynamics perspective. Using carefully conceived and illuminating color graphics, the global dynamical behaviors of the 50 (out of 256) local rules that have not yet been covered in Volumes I and II are exposed via their stunningly revealing basin tree diagrams. The Bernoulli στ-shift dynamics discovered in Volume II is generalized to hold for all 50 (or 18 globally equivalent) local rules via complex and hyper Bernoulli wave dynamics. E. | ||
| 938 | |a Askews and Holts Library Services |b ASKH |n AH24686194 | ||
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL1679749 | ||
| 994 | |a 92 |b IZTAP | ||