https://en.wikipedia.org/wiki/Moore_curve

This one is the loop version of Hilbert curve. You get a closed curve without crossing (courbe de Jordan) that fills the plane

here is L system I used (additional F in the axiom, compared to what I found in the internet...)

Alphabet: L, R

Constants: F, +, −

Axiom: FLFL+F+LFL

Production rules:

L → −RF+LFL+FR−

R → +LF−RFR−FL+

Here, F means "draw forward", − means "turn left 90°", and + means "turn right 90°" (see turtle graphics).

L=1 R=2 F=3 +=4 -=5

let me know if you have troubles to reuse or remodel it.

Next one is Hilbert Curve in 3D, hoping you are not tired...

then after, I will try to introduced the branching using L-system, but still struggling -> for trees / tree shapes

below is the curve. not easy to say that it has an interior and exterior on the plane...

below is the interior of the curve