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Define the "information function" to be I=-sum_(i=1)^NP_i(epsilon)ln[P_i(epsilon)], (1) where P_i(epsilon) is the natural measure, or probability that element i is populated, ...

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 ...

The fractal illustrated above.

A polyhedral graph having nine vertices. There are 2606 nonisomorphic nonahedral graphs, as first enumerated by Federico (1969; Duijvestijn and Federico 1981). Named ...

An oriented graph is a directed graph having no symmetric pair of directed edges. A complete oriented graph is called a tournament. The numbers of oriented graphs on n=1, 2, ...

A polyhedral graph on five nodes. There are two topologically distinct pentahedral graphs which, through duality, correspond to the skeletons of the square pyramid (left ...

A scale-free network is a connected graph or network with the property that the number of links k originating from a given node exhibits a power law distribution ...

Sea horse valley is a name sometimes given to the portion of the Mandelbrot set centered around -0.75+0.1i.

An object is said to be self-similar if it looks "roughly" the same on any scale. Fractals are a particularly interesting class of self-similar objects. Self-similar objects ...

A fractal which can be written as a Lindenmayer system with initial string "YF", string rewriting rules "X" -> "YF+XF+Y", "Y" -> "XF-YF-X", and angle 60 degrees.