Stacking and crushing
You see figures being crushed while preserving their area. Hyperbolas are involved. The two initial squares are in the golden ratio for this to work. One is a unit square while the other has a side of length phi=(1+sqrt(5))/2. See Edmund Harriss's video below for the context.
Video by Edmund Harriss and Pierre Arnoux
GIF version of the animation
What it does to the pythagorean tiling.
Animated GIF
