Wednesday, May 9, 2007
Back in the early nineties I (or I should say, my 286/12) spent many a night rendering fractals using the Fractint DOS program. Like probably everyone else into fractals, I spent a large part of my time exploring the Mandlebrot set -- one of the best known, most easily-recognized fractals.
Which is why I was both amazed and amused to learn of the Buddhabrot a couple of days ago. The same iterative series is used as is for the Mandlebrot set, but the image is colored based on the density plot of the trajectories that escape to infinity. As you can see, the images are similar to those of the Mandlebrot set only more detailed.
I was simultaneously amused, not just by the clever name, but by the fact that you have to swap the traditional axises such that the real axis is vertical and the imaginary axis is horizontal -- in other words, you have to use a non-standard orientation to make it look like a "buddha" at all. Which just goes to show that fractals are as much art as they are math.