How exactly does a random number generator work? I'd imagine it has some sort of function that inputs a logical series of numbers (the positive integers would probably be simplest) and outputs a "random" number between 0 and 1 (or 0 and 65535 or whatever). What would this function be like?
Also, what exactly are the properties that one looks for to evaluate how "random" the output is? There are definately qualitative criteria for deciding how random something is...for example, a field of points that are more dense toward the center would somehow be less random than a field with no large discernable clusters. Are there any quantitative criteria for randomness?