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A finite set of contraction maps w_i for i=1, 2, ..., N, each with a contractivity factor s<1, which map a compact metric space onto itself. It is the basis for fractal image ...

C_4 is one of the two groups of group order 4. Like C_2×C_2, it is Abelian, but unlike C_2×C_2, it is a cyclic. Examples include the point groups C_4 (note that the same ...

A random matrix is a matrix of given type and size whose entries consist of random numbers from some specified distribution. Random matrix theory is cited as one of the ...

The Menger sponge is a fractal which is the three-dimensional analog of the Sierpiński carpet. The nth iteration of the Menger sponge is implemented in the Wolfram Language ...

The field of all rational and irrational numbers is called the real numbers, or simply the "reals," and denoted R. The set of real numbers is also called the continuum, ...

Let V be a vector space over a field K, and let A be a nonempty set. Now define addition p+a in A for any vector a in V and element p in A subject to the conditions: 1. ...

Given a set X, let F be a nonempty set of subsets of X. Then F is a ring if, for every pair of sets in F, the intersection, union, and set difference is also in F. F is ...

Taking the ratio x/y of two numbers x and y, also written x÷y. Here, x is called the dividend, y is called the divisor, and x/y is called a quotient. The symbol "/" is called ...

The word "harmonic" has several distinct meanings in mathematics, none of which is obviously related to the others. Simple harmonic motion or "harmonic oscillation" refers to ...

In simple algebra, multiplication is the process of calculating the result when a number a is taken b times. The result of a multiplication is called the product of a and b, ...