Looking for help making an animation

Looking for help making an animation... by having a function turning a number into geometric shapes that scale.

I've got this idea to represent the repeating ~0.111

As fractional bits of geometric shapes so it would be (white square representing zero) . Black square, then a slightly smaller black square, and so on.

Why would I do this? I'm trying to work out ideas at the moment that aren't very clear regarding a new concept related to binary.