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?

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