Ever think about how the end box says END on it? Now, I wonder what that could mean.
You must click on it last, perhaps?
edit: oh wait..i just just pressing all the other boxes, regardless of color, and hit end last, now all of the boxes have dissapeared.
Each box begins purple. You must click the boxes one by one to turn them all white. If the last box you clicked to turn them all white was the END, then it progresses. If it was a different box, you start over. Each box controls a different set of other boxes. When you click it, they will all toggle in color. It just so happens that clicking every box an odd number of times leads to all the boxes changing color.