I have always been fascinated with Escher’s work, in particular his "Metamorphosis" woodcuts.  I’ve wanted to do something along those lines for years and finally came up with an approach.

I wrote my Scribble formula for Ultra Fractal in 2009, with something like this in mind, but I never made good use of it until now.  As you can read from the tutorial, Scribble essentially animates a rose curve along a path.  In these cases, the path was a horizontal line.  In the top image, the transition begins with a three-petal rose on the left, which morphs into a four-petal rose and then into a circle in the center.  From there, back to a three-petal rose and ending up with a four-petal rose curve.  The second image uses just four-petal roses of varying size (except for a circle in the center), and the final image uses only three-petal roses (plus a central circle).  In all, the phase angles associated with the sine and cosine functions are varied smoothly to impart a sense of rotation.