Scaling ratios and triangles in Siegel disks

Let f(z) = e(2i pi theta)z + z(2), where theta is a quadratic irrational. M cMullen proved that the Siegel disk for f is self-similar about the critica l point. We give a lower bound for the ratio of self-similarity, and we sho w that if theta = (root 5 - 1)/2 is the golden mean, then there exists a tr iangle contained in the Siegel disk, and with one vertex at the critical po int. This answers a 15 years old conjecture.