Wolfram's "Willehalm"

Author: Martin H. Jones,Timothy McFarland

Publisher: Camden House

ISBN: 9781571132116

Category: Literary Criticism

Page: 344

View: 978


New essays on Wolfram von Eschenbach's 'other' work, the neglected epic Willehalm.

A Companion to Wolfram's Parzival

Author: Will Hasty

Publisher: Boydell & Brewer

ISBN: 9781571131522

Category: Literary Collections

Page: 295

View: 3023


Up-to-date criticism and commentary on the greatest of the German courtly epics.

Characterization and Individuality in Wolfram's 'Parzival'

Author: David Blamires

Publisher: Cambridge University Press

ISBN: 9780521042710

Category: Literary Criticism

Page: 498

View: 4084


This 1966 book studies the types and techniques of character-portrayal in Parzival and of the emergence of the idea of individuality. Dr Blamires analyses each of the main characters - Gahmuret, Herzeloyde, Parzival, Gawan and Feirefiz - and shows how Wolfram presents them and the variety of methods he uses.

The Art of Recognition in Wolfram's 'Parzival'

Author: Dennis Howard Green

Publisher: Cambridge University Press

ISBN: 0521245001

Category: Literary Criticism

Page: 357

View: 4359


Discusses when recognition or non-recognition plays a part in the Parzival of Wolfram von Eschenbach.

A Nonlinear Dynamics Perspective of Wolfram's New Kind of Science

Author: Leon O Chua

Publisher: World Scientific

ISBN: 9814397563

Category: Mathematics

Page: 352

View: 4899


This penultimate volume contains numerous original, elegant, and surprising results in 1-dimensional cellular automata. Perhaps the most exciting, if not shocking, new result is the discovery that only 82 local rules, out of 256, suffice to predict the time evolution of any of the remaining 174 local rules from an arbitrary initial bit-string configuration. This is contrary to the well-known folklore that 256 local rules are necessary, leading to the new concept of quasi-global equivalence. Another surprising result is the introduction of a simple, yet explicit, infinite bit string called the super string S, which contains all random bit strings of finite length as sub-strings. As an illustration of the mathematical subtlety of this amazing discrete testing signal, the super string S is used to prove mathematically, in a trivial and transparent way, that rule 170 is as chaotic as a coin toss. Yet another unexpected new result, among many others, is the derivation of an explicit basin tree generation formula which provides an analytical relationship between the basin trees of globally-equivalent local rules. This formula allows the symbolic, rather than numerical, generation of the time evolution of any local rule corresponding to any initial bit-string configuration, from one of the 88 globally-equivalent local rules. But perhaps the most provocative idea is the proposal for adopting rule 137, over its three globally-equivalent siblings, including the heretofore more well-known rule 110, as the prototypical universal Turing machine. Contents:Period-2 Rules:Recap of Period-2 RulesBasin Tree DiagramsRobust ω-Limit Orbits of Local Rules Belonging to Group 2Quasi Global-EquivalenceSuper String S and Super Decimal xSConcluding RemarksPeriod-3, Period-6, and Permutive Rules:List of the 88 Minimal Equivalence RulesBasin Tree Diagrams, Omega-Limit Orbits and Time-τ Characteristic Function of Rules from Group 3Robust ω-Limit Orbits of Rules from Group 3Permutive RulesConcluding Remarks Readership: Graduate students, researchers and academics interested in nonlinear dynamics, computer science and complexity theory. Keywords:Cellular Automata;CNN;Chua;Wolfram;Wolfram's New Kind of Science;Computer Science;Complexity;Nonlinear Dynamics

A Nonlinear Dynamics Perspective of Wolfram's New Kind of Science

Author: Leon O. Chua

Publisher: World Scientific

ISBN: 9814317306

Category: Science

Page: 392

View: 6254


Annotation This text introduces cellular automata from a rigorous nonlinear dynamics perspective. It supplies the missing link between nonlinear differential and difference equations to discrete symbolic analysis. It provides an analysis, and classification of the empirical results presented in Wolfram's 'New Kind of Science'.

Nonlinear Dynamics Perspective Of Wolfram's New Kind Of Science, A (In 2 Volumes) - Volume Ii

Author: Leon O Chua

Publisher: World Scientific

ISBN: 9814478695

Category: Science

Page: 600

View: 6145


This novel book introduces cellular automata from a rigorous nonlinear dynamics perspective. It supplies the missing link between nonlinear differential and difference equations to discrete symbolic analysis. A surprisingly useful interpretations of cellular automata in terms of neural networks is also given. The book provides a scientifically sound and original analysis, and classifications of the empirical results presented in Wolfram's monumental ';New Kind of Science.';/a

A Nonlinear Dynamics Perspective of Wolfram's New Kind of Science

Author: Leon O Chua

Publisher: World Scientific

ISBN: 9814460893

Category: Computers

Page: 580

View: 4889


This 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 blue (for binary state 0), forming a toy universe of 256 Boolean cubes, each bearing a different vertex color combination. The corresponding collection of 256 distinct Boolean cubes are then segegrated logically into 6 distinct groups where members from each group share certain common dynamics which allow the long-term evolution of the color configuration of each bit string, of arbitrary length, to be predicted painlessly, via a toy-like gaming procedure, without involving any calculation. In particular, the evolution of any bit string bearing any initial color configuration which resides in any one of the possibly many distinct attractors, can be systematically predicted, by school children who are yet to learn arithmetic, via a simple recipe, for any Boolean cube belonging to group 1, 2, 3, or 4. The simple recipe for predicting the time-asymptotic behaviors of Boolean cubes belonging to groups 1, 2, and 3 has been covered in Vols. I, II, ..., V. This final volume continues the recipe for each of the 108, out of 256, local rules, dubbed the Bernoulli rules, belonging to group 4. Here, for almost half of the toy universe, surprisingly simple recipes involving only the following three pieces of information are derived in Vol. VI; namely, a positive integer τ, a positive, or negative, integer σ, and a sign parameter β > 0, or β < 0. In particular, given any color configuration belonging to an attractor of any one of the 108 Boolean cubes from group 4, any child can predict the color configuration after τ generations, without any computation, by merely shifting each cell σ bits to the left (resp. right) if σ > 0 (resp. σ < 0), and then change the color of each cell if β < 0. As in the five prior volumes, Vol. VI also contains simple recipes which are, in fact, general and original results from the abstract theory of 1-dimensional cellular automata. Indeed, both children and experts from cellular automata will find this volume to be as deep, refreshing, and entertaining, as the previous volumes. Contents:Bernoulli στ-Shift Rules:IntroductionBasin Tree Diagrams, Omega-Limit Orbits and Space-Time PatternsRobust and Nonrobust ω-Limit Orbits of Rules from Group 4Concluding RemarksMore Bernoulli στ-Shift Rules:IntroductionBernoulli στ-Shift RulesRobust and Nonrobust ω-Limit Orbits of Rules from Group 4Summary of Elementary 1D Cellular AutomataConcluding RemarksRemembrance of Things Past:Vignettes from Volume IVignettes from Volume IIVignettes from Volume IIIVignettes from Volume IVVignettes from Volume VVignettes from Volume VIVignettes of Metaphors from Biology, Cosmology, Physics, etc.Vignettes of 256 Boolean Cubes Readership: Students, researchers, academics as well as laymen interested in nonlinear dynamics, computer science and complexity theory. Keywords:Cellular Automata;CNN;Chua;Wolfram;Wolfram's New Kind of Science;Computer Science;Complexity;Nonlinear Dynamics