What's the minimum area of a bounding rectangle capable of accommodating a graphical representation of the nth iteration of the von Neumann universe? For n <= 3, the problem is reasonably trivial. For n = 5, the solution would be enormous (since there are 65536 sets). For n = 4, I've managed to get it down to 75 * 79, hoping for 75 * 75: http://cp4space.wordpress.com/2013/07/17/von-neumann-universe/ It should be evident that the dimensions are necessarily congruent to 3 (modulo 4). Sincerely, Adam P. Goucher