An interactive version of the rolling epicycloids described by John Baez (and others) at: http://johncarlosbaez.wordpress.com/2013/12/03/rolling-hypocycloids/ Javascript and GeoGebra versions at: http://www.malinc.se/m/RollingHypocycloids.php In order to fit inside each other, each epicycloid rotates around a point that lies on the periphery of a circle whose midpoint is the centre of the next (larger) epicycloid.
Move the white dot to rotate the cardioid, move the yellow dot to move it.