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To generate random points over the unit disk, it is incorrect to use two uniformly distributed variables r in [0,1] and theta in [0,2pi) and then take x = rcostheta (1) y = ...

Sphere tetrahedron picking is the selection of quadruples of of points corresponding to vertices of a tetrahedron with vertices on the surface of a sphere. n random ...

Replacing the logistic equation (dx)/(dt)=rx(1-x) (1) with the quadratic recurrence equation x_(n+1)=rx_n(1-x_n), (2) where r (sometimes also denoted mu) is a positive ...

Ball point picking is the selection of points randomly placed inside a ball. n random points can be picked in a unit ball in the Wolfram Language using the function ...

Given a unit circle, pick two points at random on its circumference, forming a chord. Without loss of generality, the first point can be taken as (1,0), and the second by ...

Given a triangle with one vertex at the origin and the others at positions v_1 and v_2, one might think that a random point inside the triangle would be given by ...

In the field of percolation theory, the term percolation threshold is used to denote the probability which "marks the arrival" (Grimmett 1999) of an infinite connected ...

There are at least two distinct notions of when a point process is stationary. The most commonly utilized terminology is as follows: Intuitively, a point process X defined on ...

Birthday attacks are a class of brute-force techniques used in an attempt to solve a class of cryptographic hash function problems. These methods take advantage of functions ...

The expected number of trials needed to collect a complete set of n different objects when picked at random with repetition is nH_n (Havil 2003, p. 131). For n=1, 2, ..., the ...