Buddhabrot – the last fractal?

Writing sketches for posts in the Fractals category of this blog made me realize that for many fractals (e.g. Mandelbrot, Julia, Newton etc.), visual appeal depends to a large extend on color mapping. In other words: mathematics may have blessed these fractals with a potentially beautiful complexity, but it still takes a programmer to visualize it as such.

Another thought that crossed my mind was whether the (perceived) infinite complexity of fractals couldn’t be just revealing the incompleteness of the mathematical system that produces and observes them (in which case we should name them Gödel fractals).

The above observations became manifest again when I was looking for a way to color the inside of the Mandelbrot set, that’s usually left uncolored. After a couple of very unappealing attemps, I discovered someone’s method for producing the so called Buddhabrot fractal.

 

However, as you can see, the result on my small 480×320 pixel display doesn’t even come close to some of the beautiful images that pop up in Google. Actually, it looks more like one of Marie Curie’s early X-ray images. On the other hand, I suspect that many beautiful realizations of the Buddhabrot fractal have been enhanced with the same post-processing techniques that are used for beautifying pictures of galaxies and nebulae. That feels a bit like cheating to me, because I could probably make my Buddhabrot look like Donald Trump that way… (would that still be called beautifying?)

 

Now that this somewhat demystifying idea of ‘artificial beauty’ has tempered my facination for fractals a bit, it’s time to return to the challenge of creating fast and memory-friendly algorithms for IFS-generated shapes, like space filling curves.