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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 ...

The Haferman carpet is the beautiful fractal constructed using string rewriting beginning with a cell [1] and iterating the rules {0->[1 1 1; 1 1 1; 1 1 1],1->[0 1 0; 1 0 1; ...

A fractal derived from the Koch snowflake. The base curve and motif for the fractal are illustrated below. The area enclosed by pieces of the curve after the nth iteration is ...

A simple unlabeled graph on n vertices is called pancyclic if it contains cycles of all lengths, 3, 4, ..., n. Since a pancyclic graph must contain a cycle of length n, ...

A number of fractal curves are associated with Peano. The Peano curve is the fractal curve illustrated above which can be written as a Lindenmayer system. The nth iteration ...

A "curve" (i.e., a continuous map of a one-dimensional interval) into a two-dimensional area (a plane-filling function) or a three-dimensional volume.

The triangular grid graph T_n is the lattice graph obtained by interpreting the order-(n+1) triangular grid as a graph, with the intersection of grid lines being the vertices ...

A Woodall number is a number of the form W_n=2^nn-1. Woodall numbers are therefore similar to Mersenne numbers 2^n-1 but with an additional factor of n multiplying the power ...

Compass and straightedge geometric constructions dating back to Euclid were capable of inscribing regular polygons of 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, ...

The Hanoi graph H_n corresponding to the allowed moves in the tower of Hanoi problem. The above figure shows the Hanoi graphs for small n. The Hanoi graph H_n can be ...