Sorry the truncated message. It (the link) worked with the spaces using chrome under windows 10. I copied and pasted (removing the first character) to create a new tab. On Sat, Nov 9, 2019 at 12:45 PM James Buddenhagen <jbuddenh@gmail.com> wrote:
The link with the spaces worked for me, but I cut it and pasted it to open a new tab. I removed the
On Sat, Nov 9, 2019 at 11:09 AM Paul Palmer <paul.allan.palmer@gmail.com> wrote:
The link to the Knuth paper doesn't work. (Because of spaces I think)
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
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