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Rule 30 is an elementary cellular automaton introduced by Stephen Wolfram in 1983. [2] Using Wolfram's classification scheme, Rule 30 is a Class III rule, displaying aperiodic, chaotic behaviour. This rule is of particular interest because it produces complex, seemingly random patterns from simple, well-defined rules.
In 2004, Matthew Cook published a proof that Rule 110 with a particular repeating background pattern is Turing complete, i.e., capable of universal computation, which Stephen Wolfram had conjectured in 1985. [2] Cook presented his proof at the Santa Fe Institute conference CA98 before publication of Wolfram's book A New Kind of Science.
A second way to investigate the behavior of these automata is to examine its history starting with a random state. This behavior can be better understood in terms of Wolfram classes. Wolfram gives the following examples as typical rules of each class. [4] Class 1: Cellular automata which rapidly converge to a uniform state.
Using the fact that (,) =, the generalized Marcum Q-function can alternatively be defined as a finite integral as (,) = (+) ().However, it is preferable to have an integral representation of the Marcum Q-function such that (i) the limits of the integral are independent of the arguments of the function, (ii) and that the limits are finite, (iii) and that the integrand is a Gaussian function ...
In computer science, pattern matching is the act of checking a given sequence of tokens for the presence of the constituents of some pattern. In contrast to pattern recognition, the match usually has to be exact: "either it will or will not be a match." The patterns generally have the form of either sequences or tree structures.
The basic subject of Wolfram's "new kind of science" is the study of simple abstract rules—essentially, elementary computer programs.In almost any class of a computational system, one very quickly finds instances of great complexity among its simplest cases (after a time series of multiple iterative loops, applying the same simple set of rules on itself, similar to a self-reinforcing cycle ...
The Wolfram Language (/ ˈ w ʊ l f r əm / WUUL-frəm) is a proprietary, [7] general-purpose, very high-level multi-paradigm programming language [8] developed by Wolfram Research. It emphasizes symbolic computation , functional programming , and rule-based programming [ 9 ] and can employ arbitrary structures and data. [ 9 ]
The Wolfram Demonstrations Project is an open-source collection of interactive programmes called Demonstrations. It is hosted by Wolfram Research. At its launch, it contained 1300 demonstrations but has grown to over 10,000. The site won a Parents' Choice Award in 2008.