This is equivalent to asking what the distribution of minimal interpoint distance is. This is addressed in a number of places, in particular, in this article of Tanagawa, Mochizuki, Tanaka, 1992.

Random non-intersecting circles in the plane
how to prepare clear and clarity UI design with lower image file size in photoshop for iphone UI?
In my Iphone app due to large size images my app size increased enormously.So Is there any other way to reduce the size of the images but i need the clarity shouldn't change..?
