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Rule 182 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 ...

One of the beautiful arrangements of circles found at the Temple of Osiris at Abydos, Egypt (Rawles 1997). The pattern also appears in Italian art from the 13th century ...

The sequence 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, ... (OEIS A002024) consisting of 1 copy of 1, 2 copies of 2, 3 copies of 3, and so on. Surprisingly, there exist simple formulas ...

A sequence of approximations a/b to sqrt(n) can be derived by factoring a^2-nb^2=+/-1 (1) (where -1 is possible only if -1 is a quadratic residue of n). Then ...

A map which uses a set of rules to transform elements of a sequence into a new sequence using a set of rules which "translate" from the original sequence to its ...

Universality is the property of being able to perform different tasks with the same underlying construction just by being programmed in a different way. Universal systems are ...

The matrix product of a square set of data d and a matrix of basis vectors consisting of Walsh functions. By taking advantage of the nested structure of the natural ordering ...

WireWorld is a two-dimensional four-color cellular automaton introduced by Brian Silverman in 1987. The rule for the automaton uses the cell's old value a together with the ...

Wolfram's iteration is an algorithm for computing the square root of a rational number 1<=r<4 using properties of the binary representation of r. The algorithm begins with ...

Let z=re^(itheta)=x+iy be a complex number, then inequality |(zexp(sqrt(1-z^2)))/(1+sqrt(1-z^2))|<=1 (1) holds in the lens-shaped region illustrated above. Written explicitly ...