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In continuum percolation theory, the so-called germ-grain model is an obvious generalization of both the Boolean and Boolean-Poisson models which is driven by an arbitrary ...

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 ...

Let v be a n-vector whose entries are each 1 (with probability p) or 0 (with probability q=1-p). An s-run is an isolated group of s consecutive 1s. Ignoring the boundaries, ...

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 ...

In most modern literature, a Boolean model is a probabilistic model of continuum percolation theory characterized by the existence of a stationary point process X and a ...

Brun's sieve was refined by J. B. Rosser, G. Ricci, and others.

A random-connection model (RCM) is a graph-theoretic model of continuum percolation theory characterized by the existence of a stationary point process X and a non-increasing ...

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 ...

Four or more points P_1, P_2, P_3, P_4, ... which lie on a circle C are said to be concyclic. Three points are trivially concyclic since three noncollinear points determine a ...

A topological space decomposes into its connected components. The connectedness relation between two pairs of points satisfies transitivity, i.e., if a∼b and b∼c then a∼c. ...