  A finite universe naturally supports chaotic classical motion. An ordered
fractal emerges from the chaotic dynamics which we characterize in full for a
compact 2-dimensional octagon. In the classical to quantum transition, the
underlying fractal can persist in the form of scars, ridges of enhanced
amplitude in the semiclassical wave function. Although the scarring is weak on
the octagon, we suggest possible subtle implications of fractals and scars in a
finite universe.
