2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/111596We completely characterize the conformal radii of Siegel disks in the family $$P_θ(z)=e^{2πiθ}z+z^2,$$ corresponding to {\bf computable} parameters $θ$. As a consequence, we constructively produce quadratic polynomials with {\bf non-computable} Julia sets.Dynamical SystemsComputational Complexity37F50text