  We study null geodesics of the ten-dimensional LLM geometries. In particular,
we show that there are a subset of these null geodesics that are confined to
the LLM plane. The effective dynamics of these in-plane geodesics is that of a
Hamiltonian system with two degrees of freedom (a phase space of dimension 4).
We show that these are chaotic. In the two-coloring of the LLM plane, if they
start in the empty region, they cannot penetrate the filled region and
viceversa. The dynamical problem is therefore very similar to that of a
billiards problem with fixed obstacles. We study to what extent LLM geometries
with many droplets may be treated as an incipient black hole and draw analogies
with the fuzzball proposal.
  We argue that for in-plane null geodesics deep in the interior of a region
with a lot of droplets, in order to exit towards the $AdS$ boundary they will
need to undergo a process that resembles diffusion. This mechanism can account
for signals getting lost in the putative black hole for a very long time.
