On 2015-12-25 09:51, Joerg Arndt wrote:
Added the file r07-t-5-island-split.pdf showing the splitting of the three order-7 curves (without any (3.4.6.4)-trickery) into 7 parts each.
One can spot the decomposition into 7 smaller islands and instances of what Davis/Knuth and Dekking call "carousel" (the arrangements of 6 curves with 6-fold symmetry).
Is this pertinent?
Best regards, jj
http://jjj.de/tmp-xmas/r07-t-5-island-split.pdf OMG!! You can heptasect the island in the usual way, trisect the sub- islands, and rotate them independently by π/3, as well as three overlapping sub-islands! Then Fig 6.1-C, page 52, http://jjj.de/tmp-xmas/arndt-curve-search-2015.12.25.pdf it *looks* like the figure is similar to 7/12 of itself, which is bloody impossible. Holy something, I'm confused! --Bill PS: Thanks!
* rwg <rwg@sdf.org> [Dec 23. 2015 20:26]:
Jörg, these recursive arcs are beautiful and ingenious, but in the limit, they all describe the same area-filling function, where in this case, the area filled is 1/3 of a "France Flake" island. All such area-fills map closed intervals onto closed sets, hitting *all* the points at least once, uncountably many at least twice, and at least countably many at least thrice.
Your island/3 looks to be self-similarly dissectible. Could you render a multicolored one to show how many pieces? --rwg
On 2015-12-21 07:00, Joerg Arndt wrote: [...]