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A fractal curve of infinite length which bounds an area twice that of the original square.

A fractal process for which H>1/2, so r>0.

A fractal process for which H<1/2, so r<0.

The largest n such that |z_n|<4 in a Mandelbrot set. Points of different count are often assigned different colors.

A portion of the Mandelbrot set centered around 0.3+0i with size approximately 0.1+0.1i.

The Peano-Gosper curve is a plane-filling function originally called a "flowsnake" by R. W. Gosper and M. Gardner. Mandelbrot (1977) subsequently coined the name Peano-Gosper ...

For some range of r, the Mandelbrot set lemniscate L_3 in the iteration towards the Mandelbrot set is a pear-shaped curve. In Cartesian coordinates with a constant r, the ...

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 ...

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 version of fractal dimension used in time-series analysis.