{"product_id":"9789814460897","title":"Nonlinear Dynamics Perspective Of Wolfram's New Kind Of Science, A (Volume Vi): (Volume VI)","description":"\u003cp\u003eThis 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 \u003ci\u003ecubical graph\u003c\/i\u003e in red (for binary state 1), or blue (for binary state 0), forming a toy universe of 256 \u003ci\u003eBoolean cubes\u003c\/i\u003e, each bearing a different vertex color combination.\u003c\/p\u003e\u003cp\u003eThe corresponding collection of 256 distinct \u003ci\u003eBoolean cubes\u003c\/i\u003e 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.\u003c\/p\u003e\u003cp\u003eThis final volume continues the recipe for each of the 108, out of 256, local rules, dubbed the \u003ci\u003eBernoulli rules\u003c\/i\u003e, 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 \u003ci\u003esign\u003c\/i\u003e parameter β \u0026gt; 0, or β \u0026lt; 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 \u0026gt; 0 (resp. σ \u0026lt; 0), and then change the color of each cell if β \u0026lt; 0.\u003c\/p\u003e\u003cp\u003eAs in the five prior volumes, Vol. VI also contains simple recipes which are, in fact, general and \u003ci\u003eoriginal\u003c\/i\u003e results from the abstract theory of \u003ci\u003e1-dimensional cellular automata\u003c\/i\u003e. Indeed, both children and experts from \u003ci\u003ecellular automata\u003c\/i\u003e will find this volume to be as deep, refreshing, and entertaining, as the previous volumes.\u003c\/p\u003e\u003cbr\u003e\u003cb\u003eContents:\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003eBernoulli σ\u003csub\u003eτ\u003c\/sub\u003e-Shift Rules:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eIntroduction\u003c\/li\u003e\n\u003cli\u003eBasin Tree Diagrams, Omega-Limit Orbits and Space-Time Patterns\u003c\/li\u003e\n\u003cli\u003eRobust and Nonrobust ω-Limit Orbits of Rules from Group 4\u003c\/li\u003e\n\u003cli\u003eConcluding Remarks\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003eMore Bernoulli σ\u003csub\u003eτ\u003c\/sub\u003e-Shift Rules:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eIntroduction\u003c\/li\u003e\n\u003cli\u003eBernoulli σ\u003csub\u003eτ\u003c\/sub\u003e-Shift Rules\u003c\/li\u003e\n\u003cli\u003eRobust and Nonrobust ω-Limit Orbits of Rules from Group 4\u003c\/li\u003e\n\u003cli\u003eSummary of Elementary 1D Cellular Automata\u003c\/li\u003e\n\u003cli\u003eConcluding Remarks\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003eRemembrance of Things Past:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eVignettes from Volume I\u003c\/li\u003e\n\u003cli\u003eVignettes from Volume II\u003c\/li\u003e\n\u003cli\u003eVignettes from Volume III\u003c\/li\u003e\n\u003cli\u003eVignettes from Volume IV\u003c\/li\u003e\n\u003cli\u003eVignettes from Volume V\u003c\/li\u003e\n\u003cli\u003eVignettes from Volume VI\u003c\/li\u003e\n\u003cli\u003eVignettes of Metaphors from Biology, Cosmology, Physics, etc.\u003c\/li\u003e\n\u003cli\u003eVignettes of 256 Boolean Cubes\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003c\/ul\u003e\u003cbr\u003e\u003cb\u003eReadership:\u003c\/b\u003e Students, researchers, academics as well as laymen interested in nonlinear dynamics, computer science and complexity theory.\u003cbr\u003e","brand":"World Scientific Publishing Company, Incorporated","offers":[{"title":"Default Title","offer_id":47185345118448,"sku":"9789814460897","price":34.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9789814460897_p0.jpg?v=1763692293","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9789814460897","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}