This really needs pictures. n/3584 <http://gosper.org/dragtrip3584.png>, n/3840 <http://gosper.org/dragtrip3840.png>, n/3840|n/3584 <http://gosper.org/dragtrip3840|3584.png>. (How do I add to A260482?) (Save Selection As chose an inadequate resolution. I had to replot and Export instead, even though the original plots looked great in the notebook. ?) Reminders: Only the vertices matter. The edges are just to show ordering. No vertex is on the boundary. But the triple points are actually dense, so n/7/2^n and n/15/2^n will get arbitrarily close. Now if I can just find that bleeping flowsnake bug. —rwg On Tue, Feb 20, 2018 at 6:30 PM Bill Gosper <billgosper@gmail.com> wrote:
I thought OEIS A260482, A260747..A260750 completely described the (initial) Dragon triple points, all of which have preimages a(n)/15/2^k. But I just noticed an editor's remark that there is another infinite family of the form a(n)/7/2^k. These are much less "photogenic" than the old set (e.g. gosper.org/dragtrip!.png) <http://gosper.org/dragtrip!.png> because two preimages always(?) differ by 2/7/2^k, and ~75% of them have the 3rd preimage within 4/7/2^k. But they can get "arbitrarily" lopsided:
In[508]:= undrag[(69 + 27 I)/160]
Out[508]= {1539/3584, 2551/3584, 2553/3584}
(Differences presumably limited to 40%.) Also, Julian has privately remarked that there are no irrational triple points. --rwg