Tried everything I can think of but can't make it work with chrome on my phone (android) Oh well On Sat, Nov 9, 2019, 12:05 PM rwg <rwg@ma.sdf.org> wrote:
On 2019-11-09 09:09, Paul Palmer wrote:
The link to the Knuth paper doesn't work. (Because of spaces I think)
Because of spaces where there should be brain tissue between the ears of the idiots behind xmission.com . It works in my gmail outbox. Tnx for the heads-up. You can recover by reconstructing the url in your browser's url pane. —rwg
On Sat, Nov 9, 2019, 10:58 AM Bill Gosper <billgosper@gmail.com> wrote:
Wow, both Jörg Arndt and (Dekking's student!) Arie Bos sent me photocopies of the Knuth & Davis Dragon paper. (The latter signed by Knuth! <http://gosper.org/Number representation and dragon curves Paperfolding-Knuth.pdf>) But I see no mention that the area is (SPOILER) half the square of the distance between the endpoints. It is amazing how empowering to one's intuition are Julian's Mathematica functions, which permit exploring fractal functions in the continuum. E.g., I also found a pdf colorfully dividing a Dragon's area into equal tenths <http://gosper.org/dekdrag.pdf>. —rwg
On Fri, Nov 8, 2019 at 10:21 PM Bill Gosper <billgosper@gmail.com> wrote:
Wikipedia seems not to say. I wonder if expositors of "spacefilling curves" really feel in their gut that the space is filled. Or maybe they give the area, but Wikipedia censors it as "original research".
It's probably in Knuth & Davis, Number Representations and Dragon
Curves,
of which I have at least 2 copies and can find neither.
You can guess the answer if you believe the numbers pasted on Heighway Dragon triple point <http://gosper.org/dragtrip!.png>. But there's a direct approach. (Hint: AoCP II.) (Hint <http://gosper.org/basei-1.gif>)
The Dragon's image is dense with triple points and has uncountably many double points, but I think they have measure zero, and wouldn't affect the "area" if you counted them thrice and twice. —rwg