The term Fractal was coined and popularized by Benoit B Mandelbrot. It describes a broad set of shapes. Defining characteristics include non-integer dimension, or an interesting mismatch of dimension (Hausdorff dimension strictly exceeding topological dimension), and detail at all scales or self-similarity. Fractals are frequently used in procedural content generation because self-similarity seems to mimic natural processes such as erosion and plant growth. The subdivision method also maps well onto level of detail implementations: allowing an 'infinite' amount of detail to be included by recursively subdividing the detail shown as the view point moves closer to the fractal object.

Perlin noise is a fractal algorithm.

### Code Example

A simple fractal that can be generated at any dimension takes an initial point, subdivides it by n, then randomly chooses n ^ d points. This is recursively repeated for all points selected.

Examples with dimensions 0.5, 1.0, 1.5:

For source see fractal_simple.py

### PCG Wiki References

### External Links

Fractal - Wikipedia article on Fractals.

Fractal Zoomer - PHP program which operates on fractals and returns it to the browser.

### Flickr Stream

The following images on Flickr are generated using fractals: