Smallest PV
The three letter substitution rule whose scaling is the smallest PV number, the Plastic Number which is a root of the polynomial $x^3 - x - 1 = 0$. Though it might not look it at first glance, the Rauzy fractal is connected. This can be shown using the method of A. Siegel described in [Sie04]. The Rauzy fractal:

One Dimensional
Euclidean Windowed Tiling
Self Similar Substitution
Polytopal Tiles
Plastic Number