  We explore geometric properties of the Mandelbrot set M, and the
corresponding Julia sets J_c, near the main cardioid. Namely, we establish
that: a) M is locally connected at certain infinitely renormalizable parameters
c of bounded satellite type, providing first examples of this kind; b) The
Julia sets J_c are also locally connected and have positive area; c) M is
self-similar near Siegel parameters of constant type. We approach these
problems by analyzing the unstable manifold of the pacman renormalization
operator constructed in [DLS] as a global transcendental family.
