The Resource A nonlinear dynamics perspective of Wolfram's new kind of science, Volume 4, Leon O. Chua, University of California at Berkeley, USA

A nonlinear dynamics perspective of Wolfram's new kind of science, Volume 4, Leon O. Chua, University of California at Berkeley, USA

Label
A nonlinear dynamics perspective of Wolfram's new kind of science, Volume 4
Title
A nonlinear dynamics perspective of Wolfram's new kind of science
Title number
Volume 4
Statement of responsibility
Leon O. Chua, University of California at Berkeley, USA
Creator
Author
Subject
Genre
Language
  • eng
  • eng
Summary
Volume IV continues the author's odyssey on l-D cellular automata as chronicled in Volumes I, II and III, by uncovering a novel quasi-ergodicity phenomenon involving orbits meandering among omega-limit orbits of complex (group 5) and hyper (group 6) Bernoulli rules. This discovery is embellished with analytical formulas characterizing the fractal properties of characteristic functions, as well as explicit formulas for generating colorful and pedagogically revealing isomorphic basin tree diagrams. Many new results were derived and proved by uncovering subtle symmetries endowed by various subset
Member of
Cataloging source
MiAaPQ
http://library.link/vocab/creatorName
Chua, Leon O
Dewey number
  • 511.3/5
  • 511.35
  • 515.39
Illustrations
illustrations
Index
index present
Language note
English
LC call number
QA267.5.C45
LC item number
C48 2011
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
World Scientific series on nonlinear science. Series A, Monographs and treatises
Series volume
volume 75
http://library.link/vocab/subjectName
  • Wolfram, Stephen
  • Cellular automata
  • Computational complexity
  • Dynamics
  • Nonlinear theories
Label
A nonlinear dynamics perspective of Wolfram's new kind of science, Volume 4, Leon O. Chua, University of California at Berkeley, USA
Instantiates
Publication
Copyright
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references and indexes
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
  • 1.7.7. Most rules harbor at least one Isle of Eden2. Quasi-Ergodicity; 2.1. Only complex and hyper Bernoulli-shift rules are quasi-ergodic; 2.2. Quasi-ergodicity and Gardens of Eden; 3. Fractals in 1D Cellular Automata; 3.1. All time-1 characteristic functions are fractals; 3.2. Fractals in CA additive rules; 3.2.1. Rule 60; 3.2.2. Rule 90; 3.2.3. Rule 105; 3.2.4. Rule 150; 3.3. From the time-1 characteristic function to the rule number; 3.4. Number of fractal patterns; 4. New Results about Isles of Eden; 4.1. Definitions and basic lemmas
  • 4.2. Alternate proof that rules 45 and 154 are conservative for odd lengths4.3. There are exactly 28 strictly-dissipative local rules; 4.4. Isles of Eden for rules of group 1; 5. How to Find Analytically the Basin-Tree Diagrams for Bernoulli Attractors; 5.1. Bernoulli-στ basin-tree generation formula; 5.2. A practical application of the Bernoulli στ-shift basin tree generation formula; 6. Old Theorems and New Results for Additive Cellular Automata; 6.1. Theorems on the maximum period of attractors and Isles of Eden; 6.2. Scale-free property for additive rules; 7. Concluding Remarks
  • Appendix AAppendix B; Appendix C The Classical Definitions and Definitions Based on Boolean Cubes of Permutive Rules are Equivalent; Chapter 2 PERIOD-1 RULES; 1. The Second Time Around; 1.1. Recap of Period-1 Rules; 2. Basin Tree Diagrams; 2.1. Each bit string has a decimal and a fractional code; 2.2. Attractor, basin of attraction, and basin tree; 2.3. Explicit formula for generating isomorphic basin trees; 2.4. Robustness coefficient ρ; 2.5. Genotype and phenotype; 3. Omega-Limit Orbits; 3.1. General observations on ω-limit orbits from Table 6
  • 3.2. Portraits of ω-limit orbits from the basin tree diagrams exhibited in Table 63.3. Concatenated ω-limit orbit generation algorithm; 4. Rules of Group 1 have Robust Period-1 ω-Limit Orbits; 5. Concluding Remarks; REFERENCES; INDEX
Dimensions
unknown
Extent
1 online resource (405 p.)
Form of item
online
Isbn
9786613234711
Media category
computer
Media type code
c
Specific material designation
remote
System control number
  • (CKB)3400000000016488
  • (EBL)840595
  • (OCoLC)748215453
  • (SSID)ssj0000544416
  • (PQKBManifestationID)12243256
  • (PQKBTitleCode)TC0000544416
  • (PQKBWorkID)10536145
  • (PQKB)11497361
  • (MiAaPQ)EBC840595
  • (WSP)00001560
  • (EXLCZ)993400000000016488
Label
A nonlinear dynamics perspective of Wolfram's new kind of science, Volume 4, Leon O. Chua, University of California at Berkeley, USA
Publication
Copyright
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references and indexes
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
  • 1.7.7. Most rules harbor at least one Isle of Eden2. Quasi-Ergodicity; 2.1. Only complex and hyper Bernoulli-shift rules are quasi-ergodic; 2.2. Quasi-ergodicity and Gardens of Eden; 3. Fractals in 1D Cellular Automata; 3.1. All time-1 characteristic functions are fractals; 3.2. Fractals in CA additive rules; 3.2.1. Rule 60; 3.2.2. Rule 90; 3.2.3. Rule 105; 3.2.4. Rule 150; 3.3. From the time-1 characteristic function to the rule number; 3.4. Number of fractal patterns; 4. New Results about Isles of Eden; 4.1. Definitions and basic lemmas
  • 4.2. Alternate proof that rules 45 and 154 are conservative for odd lengths4.3. There are exactly 28 strictly-dissipative local rules; 4.4. Isles of Eden for rules of group 1; 5. How to Find Analytically the Basin-Tree Diagrams for Bernoulli Attractors; 5.1. Bernoulli-στ basin-tree generation formula; 5.2. A practical application of the Bernoulli στ-shift basin tree generation formula; 6. Old Theorems and New Results for Additive Cellular Automata; 6.1. Theorems on the maximum period of attractors and Isles of Eden; 6.2. Scale-free property for additive rules; 7. Concluding Remarks
  • Appendix AAppendix B; Appendix C The Classical Definitions and Definitions Based on Boolean Cubes of Permutive Rules are Equivalent; Chapter 2 PERIOD-1 RULES; 1. The Second Time Around; 1.1. Recap of Period-1 Rules; 2. Basin Tree Diagrams; 2.1. Each bit string has a decimal and a fractional code; 2.2. Attractor, basin of attraction, and basin tree; 2.3. Explicit formula for generating isomorphic basin trees; 2.4. Robustness coefficient ρ; 2.5. Genotype and phenotype; 3. Omega-Limit Orbits; 3.1. General observations on ω-limit orbits from Table 6
  • 3.2. Portraits of ω-limit orbits from the basin tree diagrams exhibited in Table 63.3. Concatenated ω-limit orbit generation algorithm; 4. Rules of Group 1 have Robust Period-1 ω-Limit Orbits; 5. Concluding Remarks; REFERENCES; INDEX
Dimensions
unknown
Extent
1 online resource (405 p.)
Form of item
online
Isbn
9786613234711
Media category
computer
Media type code
c
Specific material designation
remote
System control number
  • (CKB)3400000000016488
  • (EBL)840595
  • (OCoLC)748215453
  • (SSID)ssj0000544416
  • (PQKBManifestationID)12243256
  • (PQKBTitleCode)TC0000544416
  • (PQKBWorkID)10536145
  • (PQKB)11497361
  • (MiAaPQ)EBC840595
  • (WSP)00001560
  • (EXLCZ)993400000000016488

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