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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.
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.
Q-analysis is a mathematical framework to describe and analyze set systems, or equivalently simplicial complexes. This idea was first introduced by Ronald Atkin in the early 1970s. This idea was first introduced by Ronald Atkin in the early 1970s.
A matchstick puzzle ("Move 1 matchstick to make the equation 6+4=4 valid") and its solution below. Matchstick puzzles are rearrangement puzzles in which a number of matchsticks are arranged into shapes or numbers, and the problem to solve is usually formulated as moving a fixed number of matchsticks to achieve some specific other arrangement.
The earliest q-analog studied in detail is the basic hypergeometric series, which was introduced in the 19th century. [1] q-analogs are most frequently studied in the mathematical fields of combinatorics and special functions. In these settings, the limit q → 1 is often formal, as q is often discrete-valued (for example, it may represent a ...
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.
A simple example is fitting a line in two dimensions to a set of observations. Assuming that this set contains both inliers, i.e., points which approximately can be fitted to a line, and outliers, points which cannot be fitted to this line, a simple least squares method for line fitting will generally produce a line with a bad fit to the data including inliers and outliers.
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 ...