What do you mean "works"? The new thing isn't a hexagon. No self-similarity. Re areas: They're the same as the original hexagon for all iterations of the construction --rwg. DMakin>Surely some mistake - the fractal version also works with hexagons ? i.e. with something of unit boundary dimension. Or am I going insane ? On 4 Oct 2013, at 21:29, Dan Asimov wrote: Guess: It's 1/21 of the large figure. --Dan On 2013-10-04, at 1:27 PM, Dan Asimov wrote: That's a really cool demo! I wonder what the area is of the triangular figure of the map-of-France at the moment the 3 "segments" first touch. --Dan On 2013-10-04, at 11:47 AM, Bill Gosper wrote: Mike Stay>That's great! May I suggest that when the area is smallest, you should give those three regions the labels 1, 2, and 3? Thanks! How's http://gosper.org/flaky.gif ? --rwg On Fri, Oct 4, 2013 at 2:41 AM, Bill Gosper <billgosper@gmail.com> wrote: Funster Gary Antonick (NYT NumberPlay) fears that the Franceflake fractal boundary paradox might be too hairy for his readers, even though Martin Gardner explained it in his original Flowsnake piece. So I made an mgif (gosper.org/flake.gif) illustrating the problem, and offering a URL for an (indirect) explanation. --rwg Re fibonachos, In[984]:= Sum[Binomial[n - k, k], {k, 0, Floor[n/2]}] Out[984]= Fibonacci[1 + n]