4 ms·

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&s

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=&axiom=A&rule-1=A%3DA%2BB-A-AB%2B&rule-2=B%3D-AB%2BB%2BA-B&rule-3=&rule-4=&rule-5=&width=400&height=400&iterations=4&angle=90&direction=left&line-width=2&padding=50&background-color=rgb(0%2C%200%2C%200)&line-segment-color=white 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 1y ago
Found a space-filling curve for the wallflower: https://onlinetools.com/math/l-system-generator?draw=ABCD&skip=&axiom=A&rule-1=A%3DC%2BD-C-CD%2B&rule-2=B%3D-CD%2BD%2BC-D&rule-3=C%3D%2BBA-A-B%2BA&rule-4=D%3DB-A%2BB%2BBA-&rule-5=&width=400&height=400&iterations=4&angle=90&direction=left&line-width=2&padding=50&background-color=rgb(0%2C%200%2C%200)&line-segment-color=white https://onlinetools.com/math/l-system-generator?draw=ABCD&sk... The previous one fills out the Koch island.
- chriskw 1y ago
  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 1y ago
    > 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.

leni536 1y ago

Found a space-filling curve for the wallflower: https://onlinetools.com/math/l-system-generator?draw=ABCD&skip=&axiom=A&rule-1=A%3DC%2BD-C-CD%2B&rule-2=B%3D-CD%2BD%2BC-D&rule-3=C%3D%2BBA-A-B%2BA&rule-4=D%3DB-A%2BB%2BBA-&rule-5=&width=400&height=400&iterations=4&angle=90&direction=left&line-width=2&padding=50&background-color=rgb(0%2C%200%2C%200)&line-segment-color=white https://onlinetools.com/math/l-system-generator?draw=ABCD&sk... The previous one fills out the Koch island.

chriskw 1y ago
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 1y ago
  > 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.