Fractal -- from Wolfram MathWorld

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 scales, but the same "type" of structures must appear on all scales. A plot of the quantity on a log-log graph versus scale then gives a straight line, whose slope is said to be the fractal dimension. The prototypical example for a fractal is the length of a coastline measured with different length rulers. The

Mandelbrot Set

Fractal Dimensions: What are they? How can they be used for Feature Extraction?, by Utkarsh Lal

Curlicue Fractal -- from Wolfram MathWorld

Fractal -- from Wolfram MathWorld

Mira Fractal -- from Wolfram MathWorld

Curlicue Fractals - JMP User Community

I Love Fractals

Fractal Fun: Tweet-a-Program Mandelbrot Code Challenge—Wolfram Blog

Douady's Rabbit Fractal -- from Wolfram MathWorld