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▲ leni536 a day ago

Got a bit nerd-sniped by this and came up with an L-system that fills out (I think) "the wallflower":

https://onlinetools.com/math/l-system-generator?draw=AB&skip...

edit: On second thought, this probably generates the other fractal, but I'm not sure.

▲leni536 13 hours ago | parent [-]

Found a space-filling curve for the wallflower:

https://onlinetools.com/math/l-system-generator?draw=ABCD&sk...

The previous one fills out the Koch island.

▲chriskw 6 hours ago | parent [-]

That's really cool! I tried to get something to work last week on pen and paper but couldn't get anything to stick. Is there a strategy you used or did you just go by feel?

Edit: just noticed how you encoded a flip (AB <--> CD) between iterations like how the matrix flips the orientation of space. Super neat!

▲leni536 4 hours ago | parent [-]

> noticed how you encoded a flip (AB <--> CD)

Exactly! There is also a less obvious relationship between A and B too: B is a A "backwards" (A rotated 180°, starting the curve from the opposite end).

The strategy was to put 5 lines on the plus sign on the sides of the 5 cells, with the idea that each line eventually fills out a neighboring cell in subsequent iterations. I found one such path that had a chance of working. Not sure if this makes sense.