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In mathematics, a knot is defined as a closed, non-self-intersecting curve that is embedded in three dimensions and cannot be untangled to produce a simple loop (i.e., the ...

A fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales. The object need not exhibit exactly the same structure at all ...

The Spencer-Brown form is a simple mathematical concept that formalizes what a mathematical object is formally identical to what it is not (Spencer-Brown 1997, pp. ix and ...

An additive cellular automaton is a cellular automaton whose rule is compatible with an addition of states. Typically, this addition is derived from modular arithmetic. ...

Define a cell in R^1 as an open interval or a point. A cell in R^(k+1) then has one of two forms, {(x,y):x in C, and f(x)<y<g(x)} (1) or {(x,y):x in C, and y=f(x)}, (2) where ...

Seeks to obtain the best numerical estimate of an integral by picking optimal abscissas x_i at which to evaluate the function f(x). The fundamental theorem of Gaussian ...

There are a number of point processes which are called Hawkes processes and while many of these notions are similar, some are rather different. There are also different ...

A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions. A line is sometimes called a straight line or, more archaically, ...

A quadratic map is a quadratic recurrence equation of the form x_(n+1)=a_2x_n^2+a_1x_n+a_0. (1) While some quadratic maps are solvable in closed form (for example, the three ...

A Riemann surface is a surface-like configuration that covers the complex plane with several, and in general infinitely many, "sheets." These sheets can have very complicated ...