Fractal

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:
fractal0.50.pngfractal1.00.pngfractal1.50.png

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:

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