We see infinite f(z) = sumn exp(i n2 z) for z in the upper half plane. The color encodes the value of the theta function. The x and y coordinates are the real and imaginary part of alpha. The animation just zooms out at time t the window in the complex plane is [-t,t] x [0,t]

m4v file. Background music credit: A Thornbirds theme by Mancini.