After reading this page from Paul Bourke I had a go at creating fractal planets by one of the methods he mentions;
1. Take a sphere of points (best to use a geodesic sphere so the points are evenly spread over the surface of the sphere).
2. Cut the sphere in half with a plane that goes through the origin. See the section on Great Circles here.
3. All points on one side of the plane are moved outwards and all points on the other are moved in.
4. Repeat this process a few hundred times and you get a fractal planet.
And here is a movie of the creation process.
Fractal planets are now included in the latest version of Visions Of Chaos.