Weird/Uncommon/Potentially Utterly Useless Builds

Okay, so a fun thought I had flying around here, is that there's builds people generally go for tons of power, and less attack speed. Generally I don't get an attack speed too high because I end up sacrificing too much damage. This made me think about potential builds, and I came across a funny thought after seeing a Yi with an attack speed of at least 2.50 and managed to decimate a turret without a minion wave.

I thought maybe what if you focused a build around pure attack speed, getting it SO ridiculously high that it'd be like a machine gun of attacks. Runes, Masteries and Item build, combined with an optimal champ pick (a ranged, like teemo?)...would all have to be considered to make this possible - but still potentially useless. How would someone get this build to work? Would be possible? Potentially hilarious experiment (or at least a fun experiment :P)?

Thoughts?

p.s. if no thoughts on this idea, maybe your own hilarious build/combination. I know 'break the meta' is slowly becoming the new meta... <XD

p.p.s this is a light hearted thread btw.