In 1990s, M.Lyubich and Y.Minsky introduced the hyperbolic 3-laminations associated with rational maps as an analogue of the hyperbolic 3-manifolds associated with Kleinian groups. In this talk I will present a new method to describe topological and combinatorial changes of laminations associated with hyperbolic-to-parabolic degeneration of quadratic maps.

The method is based on tessellation of filled Julia sets, which gives a nice organization of the dynamics inside the filled Julia set like external rays outside.