Hilbert spiral (L-system)

A Lindenmayer system that draws a sequence of growing Hilbert curves following a spiral layout.

Like in the previous experiment, a repetition rule is added to the Hilbert rules (A and B) to obtain the sequence. In order to produce the spiral layout, the rule contains some turns and different repetitions of the Hilbert rules A and B.

The objective is to find a layout that starts from a central point and grows spiraling away from it. The layout is intended to be used for creating a jigsaw treemap, so a naive spiral layout (like this one) is out of the question because of the elongated regions it would produce.

By leveraging the locality properties of the Hilbert curve, the layout presented in this example should somehow manage to both spiral away from a central point and have regions with good aspect ratios.

One downside of this approach is that the central point (in red) is likely to fall far from the figure's centroid.