(png detached) ---------- Forwarded message ---------- From: Bill Gosper <billgosper@gmail.com> Date: Mon, Aug 14, 2017 at 12:05 PM To: mathfuneavesdroppers@googlegroups.com Rohan insists that 3 is too small a horizontal magnifier for these triangular trinskys, and that someone should buckle down and add TrinskyCircularize to Corey's old package of Minsky tools. (MinskyCircularize is what mapped the green figures to the black ones in https://youtu.be/lXsVWwPa7bc .) Indeed, compare 3 with 2√3: gosper.org/trispiralrt12.png <http://gosper.org/trispiralrt12.png> So much for "only gridpoints". --rwg On Mon, Aug 7, 2017 at 4:03 AM, Bill Gosper <billgosper@gmail.com> wrote:
More generally, there is no threefold rotational symmetry. Julian's function can produce only gridpoints: ListPlot[{3, 1} # & /@ NestWhileList[{#[[1]] - Floor[64 #[[2]]/127], #[[2]]} &@ {#[[1]], #[[2]] + Floor[381 #[[1]]/128]} &@ {#[[1]] - Floor[64 #[[2]]/127], #[[2]]} &, {2, 1}, # != -{1, 4} &], AspectRatio -> 1, Axes -> False, Frame -> True] gosper.org/trinsky3spiral.png And all the arguments to the Floors are merely rational. --rwg