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A Julia set with c=-0.123+0.745i, also known as the dragon fractal.

The term "ice fractal" refers to a fractal (square, triangle, etc.) that is based on a simple generating motif. The above plots show the ice triangle, antitriangle, square, ...

A fractal curve, also called the C-curve (Gosper 1972). The base curve and motif are illustrated below. Duvall and Keesling (1999) proved that the Hausdorff dimension of the ...

A fractal composed of repeated copies of a pentagram or other polygon. The above figure shows a generalization to different offsets from the center.

Given an infinitive sequence {x_n} with associative array a(i,j), then {x_n} is said to be a fractal sequence 1. If i+1=x_n, then there exists m<n such that i=x_m, 2. If h<i, ...

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 ...

The box fractal is a fractal also called the anticross-stitch curve which can be constructed using string rewriting beginning with a cell [1] and iterating the rules {0->[0 0 ...

A fractal based on iterating the map F(x)=ax+(2(1-a)x^2)/(1+x^2) (1) according to x_(n+1) = by_n+F(x_n) (2) x_(y+1) = -x_n+F(x_(n+1)). (3) The plots above show 10^4 ...

The Mandelbar set is a fractal set analogous to the Mandelbrot set or its generalization to a higher power with the variable z replaced by its complex conjugate z^_.

The fractal-like figure obtained by performing the same iteration as for the Mandelbrot set, but adding a random component R, z_(n+1)=z_n^2+c+R. In the above plot, ...