The connectedness locus in the space of critically marked cubic polynomials with a fixed Siegel disk of the golden mean rotation number. There is an involution of this plane sending red to blue, which corresponds to swapping the two marked critical points. The common boundary is a highly intricate Jordan invariant under this involution. It can be described as the locus of all cubics with both critical points on the boundary of their Siegel disks.

For details, see Dynamics of cubic Siegel polynomials, Commun. Math. Phys. 206 (1999) 185-233.

Picture courtesy of Arnaud Cheritat (http://picard.ups-tlse.fr/~cheritat)