Earlier quoted context omitted.
Yeah, let me try to be more precise, though maybe it's worth writing down in a more formal setting because comments are awkward. Say we're looking at the Hilbert curve. I claim that for almost all physical positions, a sufficiently small change in position yields a correspondingly small change in coordinate. In the purely mathematical sense, this means something like "continuous except at points with at least one rat…
I took a 256 square hilbert curve and took random points in it (discarding points where the euclidian distance was > 8). Here is the plot: https://gist.github.com/justinvanwinkle/22a15bb33536095b05dc... Notice the Log y axis. I don't you think you could consider this even roughly continuous. This is only even bounded because I only took points within the 256x256 grid, if I let it run over say a 1000x1000 grid the hil…
I'm confused about the second plot; what order is the curve? It seems weird that there are no points between 10^12 and 10^156.