PNG is not a vector format. It is just a lossless format. I do also see loops. On Thu, May 16, 2013 at 8:14 AM, Fred lunnon <fred.lunnon@gmail.com> wrote:
I don't see David's loops; however, near the centre top of hat-crown is the hair jutting right which he mentioned. At the centre lower edge of hat-brim are two T-junctions, and there are several T-junctions elsewhere in the light regions.
All these remain distinct on zooming x8 --- presumably .PNG is a vector format permitting indefinite zooming, but nowhere to hide?
My earlier remarks may have been off-target: on more careful inspection, it becomes clear that Neil is (as hinted somewhere?) representing pixels by lattice nodes, whereas I conceived them as 4-node (black) or 0-node (white) walk segments. Furthermore, I had failed to take into account that a sequence of 0-node segments creates large rectangles, of which both spare corners P,Q might apparently overlap distant segments of the path.
[Retires wiping customary egg from face.]
Fred Lunnon
On 5/16/13, David Wilson <davidwwilson@comcast.net> wrote:
Very impressive.
I do, however, notice a few hairs and loops.
One example is a loop extending down from the top of the at just left of the hat's center, which has a hair at its bottom jutting out to the right.
I found a few other hairs and closed loops on inspection.
I realize these might be artifacts of resolution, but they might also be bugs, so thought you would like to know.
-----Original Message----- From: math-fun-bounces@mailman.xmission.com [mailto:math-fun- bounces@mailman.xmission.com] On Behalf Of Bill Gosper Sent: Thursday, May 16, 2013 7:12 AM To: math-fun@mailman.xmission.com Subject: Re: [math-fun] Hilbert(Hilbert)
NeilB>
Once we got the code working, we soon found out that it would be necessary to go down to level 9 to get a good result. [...]
Lastly, some things about the final picture could be improved. [...]
Julian uncovered a bug in Neil's code, whose repair enabled Neil to reach level 10. I hope he doesn't mind my leaking http://gosper.org/hilbert-10.png .
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