Actually, both versions of twister have rotation of coordinates occuring during the course of the MPEG. The first version undergoes a counterclockwise revolution which actually undoes the natural rotation of the function itself, allowing a closer look at the changes occuring within the spiral. The second version does a clockwise rotation which adds to the natural rotation, so it really spins out.
The x and y coordinates are not equal in these graphs: 4 units along the x axis is equal to 3 along the y axis. The unadultered function looked stretched out to me, so I compensated.