When will it hit the corner?

On the dy/dan blog there is a video with a question. Can you answer it?
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on Thursday, February 11th, 2010 at 12:02 am and is filed under Problem.
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February 11th, 2010 at 9:32 pm
From the brief glimpses of the logo given in this clip, it appears the angle out involves a bit of randomness. As a result, I don’t believe it’s possible to calculate the periodicity.
If we could only get a formula representing the path of the square, or perhaps our blog’s host could invent said formula…
February 11th, 2010 at 9:37 pm
> or perhaps our blog’s host could invent said formula…
I am not known to provide formulas.