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Update:
See my paper "Plane-filling curves on all uniform grids"
at http://arxiv.org/abs/1607.02433 for more information!
The shortened descriptions of the L-systems are in the file
short-lsys.tar.xz (4.3 MByte, unpacks to 136 MByte).
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At the
DIMACS Conference on Challenges of Identifying Integer Sequences
(Rutgers University, October 9 - 10, 2014)
I gave a talk ("There be dragons. Thousands!") about my search for
plane-filling curves generated by L-systems.
A video of my talk can be found under http://vimeo.com/album/3082332
The directories described below contain the material I promised to put online.
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Curves in the square grid (turns by +-90 degrees):
./p4/all-rNN-q-curves.pdf renderings
./c4/search-rNN-q-curves.txt L-systems
where NN is the order of the L-systems.
Curves in the triangular grid (turns by 0, +-120 degrees):
./p3/all-rNN-curves.pdf renderings
./c3/search-rNN-curves.txt L-systems
where NN is the order of the L-systems.
Curves with turns by +60 and -120 degrees:
./p6/all-rNN-b-curves.pdf renderings
./c6/search-rNN-b-curves.txt L-systems
where NN is the order of the L-systems.
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All curves where found in November and December 2013
Joerg Arndt, Oct 24 2014