Showing Web View For Page 798 | Show full page with images

Examples of multiway systems that generate different fractions of possible strings, and in effect range from being highly incomplete to highly inconsistent. The plots show what fraction of strings of a given length have been produced by each of the first 25 steps in the evolution of each multiway system. If less than half the strings of a given length are ever produced, this means that there must be some strings where neither the string nor its negation can be proved, indicating incompleteness. But if more than half the strings are produced, there must be cases where both a string and its negation can be proved, indicating inconsistency. Rules (f) through (i), however, produce exactly half the strings of any given length, and can be considered complete and consistent.

Exportable Images for This Page:

From Stephen Wolfram: A New Kind of Science [citation]