Smallest PV

Discovered by


The three letter substitution rule whose scaling is the smallest PV number, 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: rauzy fractal

Substitution Rule

Rule Smallest PV


Patch Smallest PV


Siegel, Anne
Pure discrete spectrum dynamical system and periodic tiling associated with a substitution
Ann. Inst. Fourier (Grenoble) 2004, 54, 2, pp. 341--381,