# currently rendering (lacunaries and automorphisms of the unit disk, oh my)

Setup:
Let
$v(q) = \sum_{n=1}^{\infty} (-1)^{n}q^{2^{n}}$ and
$\mathrm{mob}(\theta,q,q_{0}) = e^{i\theta} \frac{q-q_{0}}{1-\bar{q}_{0}q}$

I’m currently generating a movie depicting how $v(q)$ changes when we apply the
Mobius transformation to the unit disk $\mathbb{D}$ first and then take $v(q)$. In my
setup $q_{0}=-1/\sqrt[4]{3}$, and $\theta$ is in the interval $[0,2\pi]$ in steps of
1/1024th the length of the interval. Blake Courter said that it was
pretty easy to do this, and I’m currently at frame 459.

Video is done, here it is: