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A fractal-like structure is produced for x<0 by superposing plots of Carotid-Kundalini functions ck_n of different orders n. the region -1<x<0 is called fractal land by ...

The Cesàro fractal is a fractal also known as the torn square fractal. The base curves and motifs for the two fractals illustrated above are shown below. Starting with a unit ...

For every p, the kernel of partial_p:C_p->C_(p-1) is called the group of cycles, Z_p={c in C_p:partial(c)=0}. (1) The letter Z is short for the German word for cycle, ...

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 ...

A coordinate chart is a way of expressing the points of a small neighborhood, usually on a manifold M, as coordinates in Euclidean space. An example from geography is the ...

A Julia set with constant c chosen at the boundary of the Mandelbrot set (Branner 1989; Dufner et al. 1998, p. 225). The image above was computed using c=i.

For any alpha in A (where A denotes the set of algebraic numbers), let |alpha|^_ denote the maximum of moduli of all conjugates of alpha. Then a function ...

The "imaginary error function" erfi(z) is an entire function defined by erfi(z)=-ierf(iz), (1) where erf(z) is the erf function. It is implemented in the Wolfram Language as ...

A Julia set J consisting of a set of isolated points which is formed by taking a point outside an underlying set M (e.g., the Mandelbrot set). If the point is outside but ...

The term "fractal dimension" is sometimes used to refer to what is more commonly called the capacity dimension of a fractal (which is, roughly speaking, the exponent D in the ...