1
$\begingroup$

I'm interested in filling 2d square with space filling, non-self-intersecting, locality preserving, self-similar curves, like Hilbert curve. I found interesting work concerning three dimensional case "How many three-dimensional Hilbert curves are there?" http://www4.ncsu.edu/~njrose/pdfFiles/HilbertCurve.pdf but I need 2d.

Actually I'm looking for plane filling non-self-intersecting curves with short Lindenmayer representation. But I have no ideas how to generate all those except with brute-force. Is there any literature on the subject?

Improve this question
$\endgroup$
7
  • 1
    $\begingroup$ What do you mean by a "plane filling non-self-intersecting curve"? The paper to which you gave a link does not include this notion. $\endgroup$
    – Wlodek Kuperberg
    Oct 3, 2018 at 20:30
  • 2
    $\begingroup$ I’m pretty sure plane filling curves can’t be bijective. $\endgroup$
    – Thomas Rot
    Oct 3, 2018 at 20:44
  • 1
    $\begingroup$ @ThomasRot I meant like Hilbert curve it can self-contact without self-crossing. $\endgroup$
    – Moonwalker
    Oct 3, 2018 at 20:57
  • 2
    $\begingroup$ @WlodekKuperberg I would like curves which behave like Hilbert curve. Its limit fills the square while finite representation it is not self-intersecting and even limit case is self-contacting without self-crossing. $\endgroup$
    – Moonwalker
    Oct 3, 2018 at 21:27
  • 1
    $\begingroup$ You probably need a definition of "self crossing". $\endgroup$
    – Gerald Edgar
    Oct 4, 2018 at 0:21

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.