On 2018-07-13 23:25, Joerg Arndt wrote:
Should "coarsen" mean lower iterates, here you go: ec3464-curve-multi-decomp-it1.pdf ec3464-curve-multi-decomp-it2.pdf ec3464-curve-multi-decomp-it3.pdf // and that one is the fourth iterate: ec3464-curve-multi-decomp.pdf
Iterate zero is a hexagon.
Best regards, jj No, sorry, I meant fewer fractal pieces. But I was confused . . .
* Bill Gosper <billgosper@gmail.com> [Jul 14. 2018 08:13]:
Jörg, https://jjj.de/tmp-math-fun/ec3464-curve-multi-decomp.pdf contains a self-similar trisection of the Kochflake. Oops, no. You have two different fractal tiles here, in area ratio 3:2. Unless there's an interdissection between them, we still lack the magic trisection: slice up three flakes; reassemble into a bigger flake.
To iterate, Mandelbrot dissects the flake into subflakes, six small and one large, where the large has thrice the area of a small, which fairly begs for an actual trisection into smalls. Redissecting the large produces another small plus six very smalls, 1/3 scale. Areas 6/27 + 7/9 = 1. --Bill
How much can you coarsen it? --Bill
On Thu, Jul 12, 2018 at 8:34 PM Bill Gosper <billgosper@gmail.com> wrote:
Fortunately, I was already lying down. Shouldn't you be able to pack three copies of https://jjj.de/tmp-math-fun/ec3464-curve-tile-BBB-decomp.pdf around its lower left corner, erase the black components, and thereby get a Kochflake from six as well as three of those shapes? Wait, that doesn't add up. You need to put those black things back somehow. --rwg
On Fri, Jul 13, 2018 at 11:52 AM Bill Gosper <billgosper@gmail.com> wrote:
Jörg, https://jjj.de/tmp-math-fun/ec3464-curve-multi-decomp.pdf contains a self-similar trisection of the Kochflake. How much can you coarsen it? --Bill
On Thu, Jul 12, 2018 at 8:34 PM Bill Gosper <billgosper@gmail.com> wrote:
Fortunately, I was already lying down. Shouldn't you be able to pack three copies of https://jjj.de/tmp-math-fun/ec3464-curve-tile-BBB-decomp.pdf around its lower left corner, erase the black components, and thereby get a Kochflake from six as well as three of those shapes? Wait, that doesn't add up. You need to put those black things back somehow. --rwg