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First-passage percolation is a time-dependent generalization of discrete Bernoulli percolation in which each graph edge e of Z^d is assigned a nonnegative random variable ...

An official chessboard is an 8×8 board containing squares alternating in color between olive green and buff (where "buff" is a color variously defined as a moderate orange ...

V_t=e^(-ytau)S_tN(d_1)-e^(-rtau)KN(d_2), where N is the cumulative normal distribution and d_1,d_2=(log((S_t)/K)+(r-y+/-1/2sigma^2)tau)/(sigmasqrt(tau)). If y=0, this is the ...

In discrete percolation theory, bond percolation is a percolation model on a regular point lattice L=L^d in d-dimensional Euclidean space which considers the lattice graph ...

A deconvolution algorithm (sometimes abbreviated MEM) which functions by minimizing a smoothness function ("entropy") in an image. Maximum entropy is also called the ...

Rule 50 is one of the elementary cellular automaton rules introduced by Stephen Wolfram in 1983 (Wolfram 1983, 2002). It specifies the next color in a cell, depending on its ...

Cantor dust is a fractal that can be constructed using string rewriting beginning with a cell [0] and iterating the rules {0->[0 0 0; 0 0 0; 0 0 0],1->[1 0 1; 0 0 0; 1 0 1]}. ...

Several different types of checkerboards are used in different variants of the game of checkers. The usual checkerboard is the one used in so-called "pool checkers," also ...

The Haferman carpet is the beautiful fractal constructed using string rewriting beginning with a cell [1] and iterating the rules {0->[1 1 1; 1 1 1; 1 1 1],1->[0 1 0; 1 0 1; ...

Percolation, the fundamental notion at the heart of percolation theory, is a difficult idea to define precisely though it is quite easy to describe qualitatively. From the ...