LEADER 04455oam 2200553 450 001 9910779987003321 005 20190911112729.0 010 $a981-4460-88-5 035 $a(OCoLC)857066296 035 $a(MiFhGG)GVRL8RDA 035 $a(EXLCZ)992550000001107683 100 $a20141128h20132013 uy 0 101 0 $aeng 135 $aurun|---uuuua 181 $ctxt 182 $cc 183 $acr 200 12$aA nonlinear dynamics perspective of Wolfram's new kind of science$hVolume VI /$fLeon O. Chua, University of California at Berkeley, USA 210 $aSingapore ;$aHackensack, N.J. $cWorld Scientific$d2013 210 1$aNew Jersey :$cWorld Scientific,$d[2013] 210 4$d?2013 215 $a1 online resource (x, 568 pages) $cillustrations (chiefly color) 225 1 $aNonlinear dynamics perspective of Wolfram's new kind of science ;$vv. 6 225 1 $aWorld Scientific series on nonlinear science. Series A ;$vv. 85 300 $aDescription based upon print version of record. 320 $aIncludes bibliographical references and index. 327 $aDedication; Preface; CONTENTS; Volume VI; Chapter 1. Bernoulli ?? -Shift Rules; 1. Introduction; 1.1. Brief notes on Bernoulli ?? -shift rules; 2. Basin Tree Diagrams, Omega-Limit Orbits and Space-Time Patterns; 2.1. Basin tree diagrams and portraits of the ?-limit orbits; 2.2. Space-time patterns of Bernoulli rules using the super string as initial string; 3. Robust and Nonrobust ?-Limit Orbits of Rules from Group 4; 3.1. Robust ?-limit orbits of rules from Group 4; 3.2. Nonrobust ?-limit orbits of rules from Group 4; 4. Concluding Remarks; Chapter 2. More Bernoulli ?? -Shift Rules 327 $a1. Introduction2. Bernoulli ?? -Shift Rules; 2.1. General aspects of the Bernoulli ?? -shift rules; 2.2. Basin-tree diagrams and portraits of their ?-limit orbits; 2.3. Space-time patterns of Bernoulli rules using the superstring as initial state; 3. Robust and Nonrobust ?-Limit Orbits of Rules from Group 4; 3.1. Robust ?-limit orbits of rules from Group 4; 3.2. Non-robust ?-limit orbits of rules from Group 4; 3.3. Rules with multiple robust ?-limit orbits; 4. Summary of Elementary 1D Cellular Automata; 4.1. Boolean cubes, complexity index, and threshold of complexity 327 $a4.2. Globally and quasi-globally equivalent rules4.3. Rotations and symmetries; 4.4. Classification of the local rules; 4.5. Fractality and quasi-ergodicity; 4.6. Isles of Eden and Omega-limit orbits; 5. Concluding Remarks; Chapter 3. Remembrance of Things Past; Vignettes from Volume I; Vignettes from Volume II; Vignettes from Volume III; Vignettes from Volume IV; Vignettes from Volume V; Vignettes from Volume VI; Vignettes of Metaphors from Biology, Cosmology, Physics, etc.; Vignettes of 256 Boolean Cubes; References; Appendices 327 $aAppendix I: Correspondence between Chapters from Edited Book and Papers from IJBC JournalAppendix II: Useful and Generic Tables and Figures; Appendix III: Pages where 16 Exquisite Elementary CA Rules are Cited, Discussed, or Characterized; Appendix IV: Contents of Volumes I-VI; Index 330 $aThis invaluable volume ends the quest to uncover the secret recipes for predicting the long-term evolution of a ring of identical elementary cells where the binary state of each cell during each generation of an attractor (i.e. after the transients had disappeared) is determined uniquely by the state of its left and right neighbors in the previous generation, as decreed by one of 256 truth tables. As befitting the contents aimed at school children, it was found pedagogically appealing to code each truth table by coloring each of the 8 vertices of a cubical graph in red (for binary state 1), or 410 0$aWorld Scientific series on nonlinear science.$nSeries A,$pMonographs and treatises ;$vv. 85. 606 $aCellular automata 606 $aComputational complexity 606 $aDynamics 606 $aNonlinear theories 615 0$aCellular automata. 615 0$aComputational complexity. 615 0$aDynamics. 615 0$aNonlinear theories. 676 $a511.3/5 700 $aChua$b Leon O.$f1936-$0459925 801 0$bMiFhGG 801 1$bMiFhGG 906 $aBOOK 912 $a9910779987003321 996 $aA nonlinear dynamics perspective of Wolfram's new kind of science$93696594 997 $aUNINA 999 $bFully catalogued$aFULCAT