  We present numerical visualizations of Ricci Flow of surfaces and
3-dimensional manifolds of revolution. Ricci_rot is an educational tool which
visualizes surfaces of revolution moving under Ricci flow. That these surfaces
tend to remain embedded in R3 is what makes direct visualization possible. The
numerical lessons gained in developing this tool may be applicable to numerical
simulation of Ricci flow of other surfaces. Similarly for simple 3-dimensional
manifolds like the 3-sphere, with a metric which is invariant under the action
of SO(3) with 2-sphere orbits, the metric can be represented by a 2-sphere of
revolution, where the distance to the axis of revolution represents the radius
of a 2-sphere orbit. Hence we can also visualize the behaviour of such a metric
under Ricci flow. We discuss briefly why surfaces and 3-manifolds of revolution
remain embedded in R3 and R4 respectively, under Ricci flow and finally indulge
in some speculation about the idea of Ricci flow in the larger space of
positive definite and indefinite metrics.
