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Experimental mathematics is a type of mathematical investigation in which computation is used to investigate mathematical structures and identify their fundamental properties ...

A 4-state two-dimensional Turing machine invented in the 1980s. The ant starts out on a grid containing black and white cells, and then follows the following set of rules. 1. ...

A connective in logic known as the "exclusive or," or exclusive disjunction. It yields true if exactly one (but not both) of two conditions is true. The XOR operation does ...

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 ...

A Turing machine is a theoretical computing machine invented by Alan Turing (1937) to serve as an idealized model for mathematical calculation. A Turing machine consists of a ...

The Sierpiński sieve is a fractal described by Sierpiński in 1915 and appearing in Italian art from the 13th century (Wolfram 2002, p. 43). It is also called the Sierpiński ...

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 ...

Pascal's triangle is a number triangle with numbers arranged in staggered rows such that a_(nr)=(n!)/(r!(n-r)!)=(n; r), (1) where (n; r) is a binomial coefficient. The ...

The base-3 method of counting in which only the digits 0, 1, and 2 are used. Ternary numbers arise in a number of problems in mathematics, including some problems of ...

A k-automatic set is a set of integers whose base-k representations form a regular language, i.e., a language accepted by a finite automaton or state machine. If bases a and ...