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 , a
positive, or negative, integer , and a sign parameter > 0, or
< 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 generations,
without any computation, by merely shifting each cell bits to the
left (resp. right) if > 0 (resp. < 0), and then change the
color of each cell if < 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.
General
| Imprint: |
World Scientific Publishing Co Pte Ltd
|
| Country of origin: |
Singapore |
| Series: |
World Scientific Series on Nonlinear Science Series A, 85 |
| Release date: |
August 2013 |
| First published: |
April 2013 |
| Authors: |
Leon O. Chua
|
| Dimensions: |
279 x 216 x 32mm (L x W x T) |
| Format: |
Hardcover
|
| Pages: |
580 |
| ISBN-13: |
978-981-4460-87-3 |
| Categories: |
Books >
Science & Mathematics >
Mathematics >
Applied mathematics >
Non-linear science
|
| LSN: |
981-4460-87-7 |
| Barcode: |
9789814460873 |
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