This random project was a slightly hair-brained idea to programmatically generate one of my favorite wallpapers from iOS 7. I sometimes lose track of the background file and have to dig around to find it and one time wondered how hard it would be to programmatically generate it. (This time, I found it here.)
This program models the vertical change in pixel intensity in the foreground and background (which have different changes in intensity!) of the image using degree-3 polynomials and draws the circles in the image using alpha compositing so that circle edges are a blend of the foreground and background as a function of this vertical change. The program still isn't perfect, but only 0.06% of pixels are incorrect and all remaining pixel differences are magnitude +1 or -1 which I mostly attribute to numerical errors or the approximation that comes from modeling the vertical change in pixel intensity.
