Besides completely covering the closure of its range, a spacefilling function doubly covers an uncountable subset of it, and triple-covers a dense subset of that. (Can we define a finite "fill factor" to describe *how* dense are these subsets?) The useful idea that we're trying to express is perhaps "noncrossing", meaning that there are arbitrarily fine polygonal samplings that do self-avoid <http://gosper.org/hexpicules.png>. Could we say "self avoidable"? —rwg Another one of those "Hey, wait a minute" math posters. Julian: If you feel like it, please explain how on Earth these two brain hemispheres are born horizontally separated by exactly 10 units. Talk about agenesis corpus callosum.