Mandrian’s Fractal Art Gallery displays fractal art rendered by a sentient AI who has been roaming the Universe – possibly even the Multiverse – to bring us these wonderful pictures of far-away galaxies, planetary systems, and alien life forms. At least, I suspect there must be something in my computer intercepting my commands, I’m sure I don’t have enough artistic talent to even draw stick figures. Also you can learn about fractals – especially the famousMandelbrot Set, with some amazing deep zooms. And we have programs to generate the Mandelbrot Set à la Mondrian with music (of a kind), and to drawHarmonographs (not fractal but still pretty mathy). And some stuff in 3D! And Julia Sets, and the Burning Ship, and … well, come in and see!

I got the idea for this site when I accidentally wrote Mandrian, a program for rendering the Mandelbrot Set using Quad Trees. I didn’t know originally that my algorithm had a name, but I did suspect that such a good but simple technique could not have been thought of already. And my first draft of the program – in Python – was called Mandelbrot.py, as are hundreds of others.

The QT algorithm consists basically of subdividing an area (square in my case) into 4 equal sub-areas (squares), and then processing and evaluating them somehow, before potentially repeating the process recursively on each sub-square, if necessary. Except that recursion wasn’t ideal as it’s depth-first and I wanted breadth-first so that the image revealed top-down. So I used a queue instead.

Anyway, I digress. In order to debug and validate my program I added an option to draw borders on the squares, to make it easier to see where the program was doing stuff. That in fact didn’t really help much when the squares got small so next I tried filling the squares with random colours, and that did help. But in doing these things I noticed that the effects were quite pretty, so the debugging code became a feature.

The visual effect was reminiscent of paintings by Mondrian, so I coined ‘Mandrian’ as a portmanteau of Mandelbrot and Mondrian. Till then I’d been intending to open-source the code, but it occurred to me that maybe I could sell prints of the pictures it generated, on a website like this one. So I’ll hang on to the code a little longer (not that it’d be hard for any competent programmer to reverse-engineer!)

I’m also trying out some other fractal-generators. At the moment I’m really pleased with JWildfire by Andreas Maschke. The results have been truly impressive. I hate admitting that, if you’ve looked at some of the pictures here you might be thinking I must have a lot of artistic talent (or not). But with fractal art we’re now entering territory where computation, mathematics, and clever algorithms converge to challenge the old notions of artistic creativity. I’m more of a curator than artist.

Some of the pictures here arose almost fully-formed when I clicked the ‘Random Generation’ button, or later, the ‘Mutate’ button. I might have done some fine-tuning, such as changing the viewpoint a little, or tweaking the colours or some other parameters, but essentially I feel as if the software has given me the privilege of occasional glimpses into alien worlds. I thought that the Mandelbrot Set was bloody amazing, but seeing the fractal flame concept actually generate almost realistic-looking scenes is mind-blowing!

So please take a look around and enjoy these pictures. And I hope that you might also visit the shop (currently under construction) and spend some money 🙂