* 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
There are many ways to do this, one is http://jjj.de/tmp-xmas/gosper-tiling-by-border.pdf But you do know _that_ one (more than on page in the file!). Another one would give 21 parts, just by splitting each of the thirds into 7 similar copies. As it is past beer o'clock here I just simply uploaded http://jjj.de/tmp-xmas/arndt-curve-search.pdf I hope there is more than one instance "oh!" in there, though the text (note the \marginpars) still needs serious polishing (notably the part about complex numeration systems, I sadly may have to drop it finally). The big question about a lot of what I found is: why hasn't that been done 25 years ago? Best regards, j-ö-j <--= Umlaut!
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