WEdwinClark>I have always liked David Ullrich's picture of a space filling curve: http://www.math.okstate.edu/~ullrich/PeanoHaHa.gif Exactly! This is the only correct interpretation, which is why I object to polygonal approximations being called "spacefilling curves". On Thu, May 23, 2013 at 9:13 AM, Bill Gosper <billgosper@gmail.com> wrote: The usual discrete-sampled Peano curve self contacts, so you can't follow the path. The standard fix is to average consecutive vertices to form the median curve. Ever seen Peano's? Here's why not: http://gosper.org/fylfy-mind.png . A really pleasing design, if you're young enough. --rwg I showed http://gosper.org/fylfy-mind.png to a friend who happens to be Indian, and he enthusiastically recommended "swasthik" in Google images. He went on to explain which variety stood for marriage, and which you painted on your front stoop, etc. He was unaware of its usurpation by the Nazis! (The word comes from Sanskrit.) Conclusion: We need more Indians on math-fun. --rwg