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The tetrix is the three-dimensional analog of the Sierpiński sieve illustrated above, also called the Sierpiński sponge or Sierpiński tetrahedron. The nth iteration of the ...

Determining the length of a country's coastline is not as simple as it first appears, as first considered by L. F. Richardson (1881-1953) and sometimes known as the ...

Informally, self-similar objects with parameters N and s are described by a power law such as N=s^d, where d=(lnN)/(lns) is the "dimension" of the scaling law, known as the ...

An array A=a_(ij), i,j>=1 of positive integers is called an interspersion if 1. The rows of A comprise a partition of the positive integers, 2. Every row of A is an ...

A Lindenmayer system, also known as an L-system, is a string rewriting system that can be used to generate fractals with dimension between 1 and 2. Several example fractals ...

Let phi(t)=sum_(n=0)^(infty)A_nt^n be any function for which the integral I(x)=int_0^inftye^(-tx)t^pphi(t)dt converges. Then the expansion where Gamma(z) is the gamma ...

A topological space in which every point has a countable neighborhood system base for its neighborhood system.

If M is continuous and int_a^bM(x)h(x)dx=0 for all infinitely differentiable h(x), then M(x)=0 on the open interval (a,b).

A 60-sided polygon.

J_(nualphabeta)^mu=J_(nubetaalpha)^mu=1/2(R_(alphanubeta)^mu+R_(betanualpha)^mu), where R is the Riemann tensor.