Read Nonlinear Dynamics Perspective of Wolfram's New Kind of Science, a

Nonlinear Dynamics Perspective of Wolfram's New Kind of Science, a

Chua Leon O

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Description: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."We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Nonlinear Dynamics Perspective of Wolfram's New Kind of Science, a. To get started finding Nonlinear Dynamics Perspective of Wolfram's New Kind of Science, a, you are right to find our website which has a comprehensive collection of manuals listed.
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ISBN: 9814390526

Description: 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."We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Nonlinear Dynamics Perspective of Wolfram's New Kind of Science, a. To get started finding Nonlinear Dynamics Perspective of Wolfram's New Kind of Science, a, you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

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Nonlinear Dynamics Perspective of Wolfram's New Kind of Science, a

Nonlinear Dynamics Perspective of Wolfram's New Kind of Science, a

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