In this experiment, an icicle is grown from a rotating support over a period of about 10 hours. The support rotates every 4 minutes. Distilled water and gently stirred surrounding air were used. The icicle forms a nearly ideal self-similar shape.
Here are two more movies of growing icicles a rotating icicle with multiple tips, and of a ripply ice finger.
See Icicle morphology for a publications about these experiments.