Dave Computes Chair Fractals

The Chair Fractal leads to some surprisingly interesting doodles. The rule for this fractal is simple. Start with an L and subdivide it into 4 smaller L shapes as follows.

Subdivide each L again.

After a while, you'll see something like this.

The result is a simple aperiodic tiling. Before we make it more interesting, it's helpful to learn to draw the fractal without subdividing. Start by drawing several nested L shapes. The number of shapes should be one less than a power of 2 (e.g. 1, 3, 7, 15, 31, 63).

Draw nested L's from each corner to the center.

Continue as follows.

Eventually, a square region is filled in, with only the corner missing.

Things get more interesting when we replace each L shape by the figures shown in the top right of each image below. I have also filled in the shapes in some of these patterns.