On Sat, Dec 26, 2015 at 5:15 AM, rwg <rwg@sdf.org> wrote:
On 2015-12-25 23:02, Joerg Arndt wrote:
* rwg <rwg@sdf.org> [Dec 26. 2015 07:19]:
OK, NeilB straightened me out. The frac-12-tile, Fig 6.1-C, page 52 is *not* 1/3 of the usual Franceoid island, but rather 1/3 of a *different* Franceoid. (And not the Floppy Franceoid you get by mirror imaging alternate generations.) Island/3 is a frac-7-tile.
Yes, it is a curve of order 12 (hence cannot give the Gosper/France island): F F0F+F+F-F-F0F+F+F-F-F0F # R12-4 # symm-dr (here 0 is "no turn", aka "do nothing). The L-systems for this one and the other 943344 curves are online at: http://jjj.de/3frac/ As one tar ball: http://jjj.de/3frac/short-lsys.tar.xz (size 4.3 MByte, unpacks into a directory ./short-lsys/ of size about 140 MByte).
It probably needs a better name
than our "pepperoncino".
I gave up naming those things already at the stage of finding them with pencil and paper, when I hit the letter 'z' within one grid and order. Now "names" are non-negative numbers, the triple (number, order, grid) uniquely specifies a curve.
This one seems noteworthy.
Bonus track for eyeballing (not mentioned in the draft):
The following images are of families of curves that were constructed. In http://jjj.de/tmp-xmas/ see the files thin-*.pdf
Best regards, jj
--rwg
[...]
Well 900K curves is pretty impressive, but how about a continuum of them? When building a frac-tile, you have, at every level of recursion, the option of mirror imaging. Hence, e.g., uncountably many slight variations of "France". --rwg. "France. We're from France." --Beldar Conehead