This is related to the square pyramid thread, since it appears that the number of colors in your squares 3.xpm, 4.xpm, 5.xpm ... goes 20,35,56,84,120,165,220,286,364 ... so it appears that the color-count of n.xmp equals the number of balls in a triangular pyramid with edge n+1 balls, namely C(n+3,3) = (n+1)*(n+2)*(n+3)/6. It appears that your squares will have a square number of colors only when n=2 or n=47. But here the pyramid is triangular, not square. This is also an integer points on an elliptic curve problem. Is it in some since the same curve, or is proving this a different problem? On Thu, Apr 17, 2008 at 8:52 AM, James Buddenhagen <jbuddenh@gmail.com> wrote:
It already looks like it IS a quilt -- strange 3d effect. Also, there seems to be a bit of an optical illusion in that certain lines that must be parallel look like they are not parallel.
On Wed, Apr 16, 2008 at 11:32 PM, Jason <jason@lunkwill.org> wrote:
I tried Rich's suggestion of accumulating color with the recursion,
and... it
looks amazing! (9-11 are prettiest.) This would make a really neat quilt or stained-glass window, if you could get the materials. Actually, the window might be doable given an accurate ability to add tint to the glass -- just follow the recursions down.