05683nam 2200733I 450 991045587060332120211110182108.01-282-75753-99786612757532981-283-794-9(CKB)2490000000001626(EBL)1679749(OCoLC)879551009(SSID)ssj0000440225(PQKBManifestationID)11925781(PQKBTitleCode)TC0000440225(PQKBWorkID)10470534(PQKB)11778877(MiAaPQ)EBC1679749(WSP)00000529(Au-PeEL)EBL1679749(CaPaEBR)ebr10422555(CaONFJC)MIL275753(EXLCZ)99249000000000162620101028d2009 uy 0engur|n|---|||||txtccrA nonlinear dynamics perspective of Wolfram's new kind of scienceVolume III /Leon O. ChuaHackensack, N.J. World Scientificc20091 online resource (357 pages)World Scientific series on nonlinear science. Series A, Monographs and treatises ;v. 68Description based upon print version of record.981-283-793-0 Includes bibliographical references and indexes.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 Eden1.4.5. There are ten complex Bernoulli and eight hyper Bernoulli shift rules2. 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; 2.4.1. Highlights from Rule 18; 2.4.2. Highlights from Rule 22; 2.4.3. Highlights from Rule 54; 2.4.4. Highlights from Rule 73; 2.4.5. Highlights from Rule 90; 2.4.6. Highlights from Rule 105; 2.4.7. Highlights from Rule 122; 2.4.8. Highlights from Rule 126; 2.4.9. Highlights from Rule 146; 2.4.10. Highlights from Rule 1503. Global Analysis of Local Rule 903.1. 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; Chapter 2. More Isles of Eden; 1. The Beginning of the End; 2. Basin Tree Diagrams of Eight Hyper Bernoulli Shift Rules2.1. Highlights from rule 262.2. 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 de.nitions; 5.2. Four basic lemmas5.3. Locating points with multiple preimages5.4. 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; 5.8.1. Another Proof for Theorem 5.2; 5.8.2. Isles-of-Eden density criterion for rule 154; 5.8.3. Another Proof for Theorem 5.3; 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 RemarksErrata for Volume IVolume 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. EWorld Scientific series on nonlinear science.Series A,Monographs and treatises ;v. 68.Cellular automataComputational complexityDynamicsNonlinear theoriesCellular automata.Computational complexity.Dynamics.Nonlinear theories.006.32511.3/5511.35Chua Leon O.1936-459925MiAaPQMiAaPQMiAaPQ9910455870603321A nonlinear dynamics perspective of Wolfram's new kind of science1899476UNINAFully cataloguedFULCAT