Polyspiral
A polyspiral is a spiral made of multiple line segments, whereby each segment is larger (or smaller) than the previous one by a given amount. Each segment also changes direction at a given angle.
If you see the effect, you'd think that there's a lot of code involved, but it's actually a very simple loop. In pseudo code, from the Rosetta Code task I created, a few years back:
set incr to 0.0
// animation loop
WHILE true
incr = (incr + 0.05) MOD 360
x = width / 2
y = height / 2
length = 5
angle = incr
// spiral loop
FOR 1 TO 150
drawline
change direction by angle
length = length + 3
angle = (angle + incr) MOD 360
ENDFOR
It takes a while to get up to speed, but it's quite spectacular.