This is a demonstration of my upcoming (free) iPad/iPhone app called 'Superformula'.
This app allows you to explore the universe of supershapes in a convenient way.
Swiping the display will let you discover the 12 dimensional parameter space. You can even use a music track to use for exploration. The music will be transformed into the frequency domain, and the energies in the frequency bands will be used to set the superformula parameters m,n1,n2,n3,a,b.
The music in this video is by Jonathan Geer.