On Sun, Jun 17, 2012 at 5:20 PM, Bill Gosper <billgosper@gmail.com> wrote:
For some pictorial. mildly trick questions: http://gosper.org/foupent.pdf (1.6M) --rwg
The scheme that makes the pentagram from pentaflakes and heptagram from heptaflakes doesn't work for even polygons--your choice is untapered or curled arms (or binary trees instead of arms). I asked Julian if the enneagram worked and he said only with overlap, and made this peculiar figure <http://gosper.org/octaflake.png> showing that eight was the highest nonoverlap case, with Cantor sets of octaflakes formed where two larger octaflakes touch side-to-side. I don't recognize the implied limiting fractal, but note that the construction does not coerce ever smaller flakes. It appears you can instead start adding ever larger ones. Maybe even after reaching the fractal limit. Maybe even asymmetrically? A playworthy shape. --rwg