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Code 2040 is a totalistic cellular automaton that yields patterns with seemingly random features. The rules and 300 steps of this automaton are illustrated above.

Code 912 is a totalistic cellular automaton that yields patterns with seemingly random features. The rules and 300 steps of this automaton are illustrated above.

A discrete distribution of a random variable such that every possible value can be represented in the form a+bn, where a,b!=0 and n is an integer.

The fractal-like figure obtained by performing the same iteration as for the Mandelbrot set, but adding a random component R, z_(n+1)=z_n^2+c+R. In the above plot, ...

The small world problem asks for the probability that two people picked at random have at least one acquaintance in common.

A theorem from information theory that is a simple consequence of the weak law of large numbers. It states that if a set of values X_1, X_2, ..., X_n is drawn independently ...

Covariance provides a measure of the strength of the correlation between two or more sets of random variates. The covariance for two random variates X and Y, each with sample ...

If the random variates X_1, X_2, ... satisfy the Lindeberg condition, then for all a<b, lim_(n->infty)P(a<(S_n)/(s_n)<b)=Phi(b)-Phi(a), where Phi is the normal distribution ...

An algorithm for multiplying two 32-bit integers modulo a 32-bit constant without using any intermediates larger than 32 bits. It is also useful in certain types of random ...

Reversion to the mean, also called regression to the mean, is the statistical phenomenon stating that the greater the deviation of a random variate from its mean, the greater ...