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 . --rwg
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 .
--rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
----- No virus found in this message. Checked by AVG - www.avg.com Version: 2013.0.3336 / Virus Database: 3162/6327 - Release Date: 05/15/13
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 .
--rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
----- No virus found in this message. Checked by AVG - www.avg.com Version: 2013.0.3336 / Virus Database: 3162/6327 - Release Date: 05/15/13
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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 .
--rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
----- No virus found in this message. Checked by AVG - www.avg.com Version: 2013.0.3336 / Virus Database: 3162/6327 - Release Date: 05/15/13
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_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
I don't have image editing application that will load a PNG, but presumably, if you loaded the image into such an application, then "bucket filled" with a color (say red), on both sides of the line, it would paint most of the picture red, except for the few small loops I mentioned.
-----Original Message----- From: math-fun-bounces@mailman.xmission.com [mailto:math-fun- bounces@mailman.xmission.com] On Behalf Of quad Sent: Thursday, May 16, 2013 6:41 PM To: math-fun Subject: Re: [math-fun] Hilbert(Hilbert)
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 .
--rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
----- No virus found in this message. Checked by AVG - www.avg.com Version: 2013.0.3336 / Virus Database: 3162/6327 - Release Date: 05/15/13
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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David Wilson:
if you loaded the image into such an application, then "bucket filled" with a color (say red), on both sides of the line, it would paint most of the picture red, except for the few small loops I mentioned.
Filling on one side of a line suffices: http://chesswanks.com/pot/hilbert10red.jpg
I didn't realize converting to a jpg would make the picture end up as a 12.5 MB file. Here's the equivalent png at less than 0.8 MB: http://chesswanks.com/pot/hilbert10red.png
Bucket filling --- neat trick! WFL On 5/17/13, Hans Havermann <gladhobo@teksavvy.com> wrote:
I didn't realize converting to a jpg would make the picture end up as a 12.5 MB file. Here's the equivalent png at less than 0.8 MB:
http://chesswanks.com/pot/hilbert10red.png _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
It's hard to imagine a picture that would be a worse JPG candidate. Two colors, lots of edges.
-----Original Message----- From: math-fun-bounces@mailman.xmission.com [mailto:math-fun- bounces@mailman.xmission.com] On Behalf Of Hans Havermann Sent: Thursday, May 16, 2013 8:37 PM To: math-fun Subject: Re: [math-fun] Hilbert(Hilbert)
I didn't realize converting to a jpg would make the picture end up as a 12.5 MB file. Here's the equivalent png at less than 0.8 MB:
http://chesswanks.com/pot/hilbert10red.png _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
----- No virus found in this message. Checked by AVG - www.avg.com Version: 2013.0.3336 / Virus Database: 3162/6332 - Release Date: 05/17/13
To rwg: I hope I didn't come off as overly critical. It's just the math geek in me looking for perfection. In truth the flaws are minor in comparison to the impressive achievement.
-----Original Message----- From: math-fun-bounces@mailman.xmission.com [mailto:math-fun- bounces@mailman.xmission.com] On Behalf Of David Wilson Sent: Thursday, May 16, 2013 8:12 PM To: 'math-fun' Subject: Re: [math-fun] Hilbert(Hilbert)
I don't have image editing application that will load a PNG, but presumably, if you loaded the image into such an application, then "bucket filled" with a color (say red), on both sides of the line, it would paint most of the picture red, except for the few small loops I mentioned.
-----Original Message----- From: math-fun-bounces@mailman.xmission.com [mailto:math-fun- bounces@mailman.xmission.com] On Behalf Of quad Sent: Thursday, May 16, 2013 6:41 PM To: math-fun Subject: Re: [math-fun] Hilbert(Hilbert)
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 .
--rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
----- No virus found in this message. Checked by AVG - www.avg.com Version: 2013.0.3336 / Virus Database: 3162/6327 - Release Date: 05/15/13
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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----- No virus found in this message. Checked by AVG - www.avg.com Version: 2013.0.3336 / Virus Database: 3162/6329 - Release Date: 05/16/13
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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participants (5)
-
Bill Gosper -
David Wilson -
Fred lunnon -
Hans Havermann -
quad