  I consider a landscape containing three vacua and study the topology of
global spacelike slices in eternal inflation. A discrete toy model, which
generalizes the well studied Mandelbrot model, reveals a rich phase structure.
Novel phases include monochromatic tubular phases, which contain crossing
curves of only one vacuum, and a democratic tubular phase, which contains
crossing curves of all three types of vacua. I discuss the generalization to
realistic landscapes consisting of many vacua. Generically, the system ends up
in a grainy phase, which contains no crossing curves or surfaces and consists
of packed regions of different vacua. Other topological phases arise on the
scale of several generations of nucleations.
