People appear not be a space filling curve anymore. It looked that way prior to the Industrial Revolution and the advent of Birth Control. But it doesn't look like people will infinitely fill all space available to them anymore. Perhaps it's because we're running out of space (artificially, by not building) in places where there's till opportunity. But I'm not sure we have convincing evidence of that. We do have evidence that people aren't wildly reproducing in almost every advanced economy, though.