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In 1704, Sebastien Truchet considered all possible patterns formed by tilings of right triangles oriented at the four corners of a square (Wolfram 2002, p. 875). Truchet's ...

Percolation theory deals with fluid flow (or any other similar process) in random media. If the medium is a set of regular lattice points, then there are two main types of ...

Sylvester's four-point problem asks for the probability q(R) that four points chosen at random in a planar region R have a convex hull which is a quadrilateral (Sylvester ...

Let a set of random variates X_1, X_2, ..., X_n have a probability function P(X_1=x_1,...,X_n=x_n)=(N!)/(product_(i=1)^(n)x_i!)product_(i=1)^ntheta_i^(x_i) (1) where x_i are ...

Informally, the sample space for a given set of events is the set of all possible values the events may assume. Formally, the set of possible events for a given random ...

The average distance between two points chosen at random inside a unit cube (the n=3 case of hypercube line picking), sometimes known as the Robbins constant, is Delta(3) = ...

Let Pi be a permutation of n elements, and let alpha_i be the number of permutation cycles of length i in this permutation. Picking Pi at random, it turns out that ...

A measure nu of a strange attractor which allows the presence of chaos to be distinguished from random noise. It is related to the capacity dimension D and information ...

Let two points x and y be picked randomly from a unit n-dimensional hypercube. The expected distance between the points Delta(n), i.e., the mean line segment length, is then ...

The Cauchy distribution, also called the Lorentzian distribution or Lorentz distribution, is a continuous distribution describing resonance behavior. It also describes the ...