  We study the rendezvous problem for two robots moving in the plane (or on a
line). Robots are autonomous, anonymous, oblivious, and carry colored lights
that are visible to both. We consider deterministic distributed algorithms in
which robots do not use distance information, but try to reduce (or increase)
their distance by a constant factor, depending on their lights' colors.
  We give a complete characterization of the number of colors that are
necessary to solve the rendezvous problem in every possible model, ranging from
fully synchronous to semi-synchronous to asynchronous, rigid and non-rigid,
with preset or arbitrary initial configuration.
  In particular, we show that three colors are sufficient in the non-rigid
asynchronous model with arbitrary initial configuration. In contrast, two
colors are insufficient in the rigid asynchronous model with arbitrary initial
configuration and in the non-rigid asynchronous model with preset initial
configuration.
  Additionally, if the robots are able to distinguish between zero and non-zero
distances, we show how they can solve rendezvous and detect termination using
only three colors, even in the non-rigid asynchronous model with arbitrary
initial configuration.
