By Leon O. Chua
Quantity IV maintains the author's odyssey on l-D mobile automata as chronicled in Volumes I, II and III, via uncovering a singular quasi-ergodicity phenomenon related to orbits meandering between omega-limit orbits of complicated (group five) and hyper (group 6) Bernoulli principles. This discovery is decorated with analytical formulation characterizing the fractal houses of attribute services, in addition to particular formulation for producing colourful and pedagogically revealing isomorphic basin tree diagrams. Many new effects have been derived and proved through uncovering sophisticated symmetries endowed through a number of subsets of the 256 Boolean cubes. For the 1st time, rigorous analyses have been used to spot sixty seven, out off 256 , neighborhood principles whose asymptotic behaviors include powerful period-l orbits. The spotlight of this carrying on with odyssey is the invention of an remoted period-3240 Isle of Eden hidden one of the dense omega-limit orbits of Wolfram's notable "random quantity producing" rule 30. this is often the most important gem identified to-date and readers are challenged to discover even higher ones.