  Einstein's field equations in general relativity admit a variety of solutions
with spacetime singularities. Numerical relativity has recently revealed the
properties of somewhat generic spacetime singularities. It has been found that
in a variety of systems self-similar solutions can describe asymptotic or
intermediate behaviour of more general solutions in an approach to
singularities. The typical example is the convergence to an attractor
self-similar solution in gravitational collapse. This is closely related to the
cosmic censorship violation in the spherically symmetric collapse of a perfect
fluid. The self-similar solution also plays an important role in critical
phenomena in gravitational collapse. The critical phenomena are understood as
the intermediate behaviour around a critical self-similar solution. We see that
the convergence and critical phenomena are understood in a unified manner in
terms of attractors of codimension zero and one, respectively, in
renormalisation group flow.
