Inspired by Vi Hart’s post about 3D printing an Apollonian gasket, I started to wonder whether it would be possible to get to that deeply Apollonian form through something more, well, Dionysian.
After Xiao mentioned Zhuangzi’s lovely dream of the butterfly yesterday, I started thinking about the relationship (which has been discussed by many philosophers) between Dionysus, the god of beautiful chaos, and Apollo, the god of rational beauty.
And I decided I would take a butterfly on a journey to attain a state of Apollonian perfection, but only after it has traveled through the chaos of dreams.
After playing around with some fractal programming, I found a suitable way to create and transform a mathematically defined butterfly (click on the image below to see the result). The cycle repeats endlessly because, of course, journeys in dreams are never finished.