Description

Fractal Subdivision is the process of repeatedly applying a set of rules that recursively subdivide space into smaller and smaller areas.

Algorithm

The first step is to define the "pattern" that will be used to subdivide space. There is no requirement that this pattern be square, but for ease of illustration those presented here will all be square. Within that pattern it is then necessary to define sub-areas where either 1) the fractal subdivision process is considered complete and no further subdivision will occur, or 2) further subdivision should occur.

Shown here are the results of a pattern of 2x2 cells where the rule is: leave the upper-left cell alone and subdivide the other three. The process is shown through four depths of recursion. In general, recursion would continue until some practical limit had been reached, such as trying to work in an area smaller than a single pixel.

Above is a simple pattern where the rule is: leave the top half alone and subdivide the bottom two quarters. Even more variety can be formed by modifying the pattern rules at subsequent depths of recursion.

Here the same pattern is again used, however it is flipped vertically on every other iteration. So on the first iteration the top half is left alone. On the second iteration the bottom half is left alone. And so on. Additional variety can be achieved by flipping horizontally (mirroring) or flipping both horizontally and vertically, or rotating 90 degrees in either direction.

Applications

Perhaps the most interesting use of the divided space is when they are filled with something other than simple filled rectangles. For instance, a bitmap...

...or text, as was done with the question mark on the "Odds And Ends" Banner.

...or some custom drawn graphic, as was done with the Pixel Robots T-Shirt design.

Wallpaper

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