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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.
Matching pursuit should represent the signal by just a few atoms, such as the three at the centers of the clearly visible ellipses. Matching pursuit (MP) is a sparse approximation algorithm which finds the "best matching" projections of multidimensional data onto the span of an over-complete (i.e., redundant) dictionary .
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 ]
WolframAlpha (/ ˈ w ʊ l f. r əm-/ WUULf-rəm-) is an answer engine developed by Wolfram Research. [3] It is offered as an online service that answers factual queries by computing answers from externally sourced data.
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.
Wolfram Alpha: Wolfram Research: 2009 2013: Pro version: $4.99 / month, Pro version for students: $2.99 / month, ioRegular version: free Proprietary: Online computer algebra system with step-by step solutions. Xcas/Giac: Bernard Parisse 2000 2000 1.9.0-99: May 2024: Free GPL: General CAS, also adapted for the HP Prime. Compatible modes for ...
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.
The q-Pochhammer symbol is closely related to the enumerative combinatorics of partitions.The coefficient of in (;) = = is the number of partitions of m into at most n parts.