Interactive rolling hypocycloids

An interactive version of the rolling hypocycloids described by John Baez (and others) at: In order to fit inside each other, each hypocycloid rotates around a point that lies on the periphery of a circle whose midpoint is the centre of the next (larger) hypocycloid.
Move the white dot! The Javascript version is a tad slow. If possible try with Java Applet, or download the worksheet.