On the math side of things, I’ve finally worked out a scheme to produce more evenly distributed paths through the fractals. I’ve two minds about this. On one hand, the outlines of the images are more thoroughly filled out, on the other the image is missing some of the nebulous detail I liked in the previous rendering image. I love this. It means I get to choose how each rendering looks. Right now I can choose between a distribution which is evenly selected per transformation or the area traced out by that map. Either the senate or the house of representatives in political terms. Each choice produces a different set of images and I am free to choose the ones that I like best.
So I’ll be playing with those choices and an infinitude in-between. I’ve also got my eye on creating something that will let my viewers create and share images of their own, as well as get into the nitty gritty details of how these images are generated and all the mathematics that goes into them.
Far from being vacuous beauties, there are a number of advanced mathematical concepts that can be explored through them. Topology, probability, measures, geometry, chaos theory, group theory are just the tip of the iceberg. I’ve plans to delve into group theory and generating one dimensional fractals, though it’s going to be a challenge for me. I’ve been more comfortable with short descriptions of the code that I’ve generated, and now I’ll be focusing on the mathematics behind them; I’ll probably be spending a lot more time on those.
Link to the gratuitous new version of the engine here: