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A catastrophe which can occur for four control factors and one behavior axis. The butterfly catastrophe is the universal unfolding of the singularity f(x)=x^6 of codimension ...

A cellular automaton is a collection of "colored" cells on a grid of specified shape that evolves through a number of discrete time steps according to a set of rules based on ...

Given a set S with a subset E, the complement (denoted E^' or E^_) of E with respect to S is defined as E^'={F:F in S,F not in E}. (1) Using set difference notation, the ...

The geodesics in a complete Riemannian metric go on indefinitely, i.e., each geodesic is isometric to the real line. For example, Euclidean space is complete, but the open ...

A family gamma of nonempty subsets of X whose union contains the given set X (and which contains no duplicated subsets) is called a cover (or covering) of X. For example, ...

A cusp catastrophe is a catastrophe which can occur for two control factors and one behavior axis. The cusp catastrophe is the universal unfolding of the singularity f(x)=x^4 ...

Fractran is an algorithm applied to a given list f_1, f_2, ..., f_k of fractions. Given a starting integer N, the FRACTRAN algorithm proceeds by repeatedly multiplying the ...

One of the beautiful arrangements of circles found at the Temple of Osiris at Abydos, Egypt (Rawles 1997). The pattern also appears in Phoenician art from the 9th century BC ...

The hemicube, which might also be called the square hemiprism, is a simple solid that serves as an example of one of the two topological classes of convex hexahedron having 7 ...

If a subgroup H of G has a group representation phi:H×W->W, then there is a unique induced representation of G on a vector space V. The original space W is contained in V, ...