My wife tried to reproduce some of the Vi's great drawings, but small errors in the angle quickly added up gave poor results. That's when the programmer in me couldn't help automatizing it in the computer, and what best that to do it in GIMP?
So, I ended up doing a very simple Python script for GIMP (my first one!) that let's you create such golden-ratio spiral figures from a single image. For instance, you can use a petal to create a flower, or, as in this example, a leave to create a plant.
You can even create an animation, sending something down a spiral fall (this time the object is not rotated by the golden-angle, but by a smaller one)
You can get the script from the GIMP's plugin registry. Enjoy and leave any interesting results at the registry's entry page.