# Env

· · learn more# ◌ Arabesques on the complex plane

21 January 2009

I’ve been playing with NodeBox lately and happily, but it was dull to wait several minutes for a tiny burning ship to render. So it was time for my twice-yearly–ish session with my nemesis, C. I say a lot of harsh things about that language, and mean them, but it is fast. With one page of code, it even compiles fast enough that I can pretend it’s interpreted. The ship:

This reminded me of a friend of a friend’s idea for a para–chaos-game generating a heatmap of simple numbers. Here’s a chart of where you’re likely to end up if you start at the origin and make 20 moves, choosing randomly from going right 1, going to your complex reciprocal, or rotating 90° counterclockwise around the origin (and, once you finish, coloring your point redder, bluer, or greener depending on your last move):

I could point my eyes at that for a time. Here’s with R, G, B = z+`i`, z×`i`, and z^{i} – it’s hard to make out, but the blue channel is doing some amazing spirals:

You can easily find more unbalanced figures. With `i`^{z}, z^{i}, and z×`i`:

Or, with `i`^{z}, z×`i`, and ln(z)+`i`, what seems to be a palimpsest renaissance architecture sketchbook floating in space:

Now I want a book on group theory, assuming that’s what I want.