spirally happiness

[aamcnamara]

Yesterday I worked on As Large As Alone for about another half hour. (Time: such a better way to measure revision progress!)

Today there was no writing. My math professor hinted in class yesterday about how we could explore generalizing what we'd been saying about the iteration of linear functions to the complex numbers, and about an hour and a half later I sat up in the middle of physics and went "fractal-like things!" and basically rushed back to my room to start working.

With a short break for lunch and physics lab and going in to see my professor and say "fractals! Complex numbers!" at him, that is. He gave me a few more hints, and since then I have been spending pretty much every spare moment contemplating complex numbers.

In brief, what I have learned over the course of the past day and a half:
- you can treat complex numbers like vectors.
- if you want to get a logarithm of a complex number, stick it in polar coordinates.
- you can treat complex numbers like vectors.
- unlike real-number iterated linear functions, which if they converge just sort of edge up on the value, complex iterated linear functions that converge spiral inward toward their destination.

Math = so cool.