For people interested in algorithmic art, I can heavily recommend the nature of code, a free ebook (also available in print) that translates many natural phenomenon into code, physics, vectors, cellular automata, fractals and more! http://natureofcode.com/book/chapter-3-oscillation/

Floraform is another tool for exploring differential growth http://n-e-r-v-o-u-s.com/blog/?p=6721

Reminds me of this great piece of digital art using differential growth algorithms: https://www.youtube.com/watch?v=9HI8FerKr6Q

There appears to be work in progress on a shape generator app that presumably uses the same algorithms: https://www.youtube.com/watch?v=DbMlrigvVZk

> In brief; we start of with a number of connected nodes in a circle. Gradually we introduce new nodes on the line—prioritizing segments where the curve bends more sharply. Over time the curve grows increasingly intricate, but it never self-intersects.

Is there a proof showing that it will never self-intersect?

Nope. It might happen. There is no comprehensive system to avoid collisions. (I'm the one who wrote the code)

Reminds me of Ricci flow [1], though done in reverse.

[1] https://en.wikipedia.org/wiki/Ricci_flow

I'm enjoying all of http://inconvergent.net/

I especially like how many of these algorithms look like ink illustrations (e.g. "Tree"). Glad it's MIT licensed.

The second line like the density of rods/cones in the retina. Also looks a lot like a space filling curve. In short this looks like it could make an interesting data structure...

That would make a neat drinks coaster.