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.
