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 * 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: [...]