Abstract
Wolframfs monumental best seller entitled gA new kind of scienceh was based almost entirely on brute-force computer simulations. In sharp contrast, this lecture presents a rigorous analytical theory based on attractors from a nonlinear dynamics perspective. New results and concepts to be presented include the partitioning (via Felix Kleinfs Vierergruppe) of all 256 local Boolean rules studied empirically by Wolfram into 88 global equivalence classes, one of which contains 4 topologically-conjugate rules capable of universal computation, and endowed with a 1/f spectrum. Another major result is the rigorous characterization of the time-asymptotic dynamics (attractors) of 112 local rules via an explicit generalized Bernoulli shift formula. Even more surprising, we have discovered the attractors of 170 local rules are blessed with the remarkable property of time-reversality. For such rules, the past evolution in time can be recovered from the future evolutions of a corresponding gtwinh rule. Only 86 local rules exhibit an garrow of timeh. One of our most fascinating discoveries is a new phenomenon, dubbed an gIsle of Eden,h having no counter part in hyperbolic differential equations, which has neither a past, nor a future! In addition to providing a mathematical foundation for brainlike dynamics, the discoveries cited above provide simple dynamical mechanism for mimicking many exotic phenomena from brain science, quantum physics, cosmology, etc.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chua, L. (2008). What’s New in Wolfram’s New Kind of Science?. In: Umeo, H., Morishita, S., Nishinari, K., Komatsuzaki, T., Bandini, S. (eds) Cellular Automata. ACRI 2008. Lecture Notes in Computer Science, vol 5191. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79992-4_2
Download citation
DOI: https://doi.org/10.1007/978-3-540-79992-4_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-79991-7
Online ISBN: 978-3-540-79992-4
eBook Packages: Computer ScienceComputer Science (R0)