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|George W. Hart||2002-08-05 15:43:24+00|
|Wonderful project! Now, can you make a drawing program which allows the user to draw any scene, and includes a provision for specifying a rectangle which displays as a recursive version of the entire drawing. Then the result can be output as an animation using any of your grids. This would allow any of us to play at being Escher...|
|Shimon Peres||2002-08-05 13:47:25+00|
|Laura Donaldson||2002-08-03 16:49:15+00|
|Hello, I am a student at Antioch University Seattle. In our math class, we just learned about fractiles. Could this piece be considered part of this theory?
I am a novice concerning these images. However, I thoroughly enjoyed going through the program. I am emailing this address to my instructor. Thank you for sharing. Laura Donaldson|
It is so wonderfull, before i've seen it I was blind.It opened my eyes so wide.Thank you|
|Rod McCallum||2002-08-03 13:32:57+00|
|Wow. Who needs drugs to twist their brain? :-)
Impressive. Fine work. Fine site. Well done.|
|Wendi Boettcher||2002-08-03 00:10:10+00|
|P H E N O M E N A L !!!
|David B$||2002-08-02 21:13:36+00|
|The animations you have created are stunning indeed. Thanks for providing not just the "spiraling" version but the "right-angle" version as well. It makes the fractal relationship even more apparent. I've been fascinated by self-reference and recursion ever since reading Hofstadter's Gödel, Escher, Bach nearly 20 years ago, and your site makes the links between the art and the mathematics even more clear than in that monumental work. What an insightful use of the available technology--thank you!|
|Martin J. Rosenblum||2002-08-01 22:03:07+00|
|Great job! I have a block about recursive stuff, and I'm still working on the conformal map, but you've given us scads to digest, recursively! Thanks, so much! -Marty|
|d r||2002-08-01 21:35:32+00|
|Hitl: what Lincl had to have said to beget assasination|
|Bob Faulkner||2002-08-01 21:19:51+00|
|Is it Art? or Science? Yes! and Yes!!
I've never before seen a more stunning combination of the two. Your work does for Escher's 'Print Gallery' what T.S. Eliot's notes do for 'The Waste Land' -- make it all so completely comprehensible -- but even better.
Thank you for so generously sharing your talent and effort.
Now, make the reptiles crawl on and off the pad, the monks ascend and descend the stairs, the water flow upward and fall, and all the other marvelous illusions move within their permuted quasi-realities -- as screen savers. You're holding a gold mine in your hands; please, don't disinterestedly walk away from it.|
|Steve Lehar||2002-08-01 13:31:37+00|
|Wonderful! Beautiful! Excellent!
Next: do the calculation in a 3-D space instead of in the flat picture plane. That way, in the animation, you would see relative motion between nearer and farther objects. For example the frame of the "greenhouse" around the gallery would move relative to the frame of the picture behind it, giving a dynamic sensation of 3-D depth, with the picture in the painting repeatedly bursting out of the 2-D picture plane and enveloping the viewer all around.
Can it be done?
|Arko Ghosh||2002-08-01 04:06:00+00|
|Mike ||2002-08-01 03:23:14+00|
|Spectacular work...it is a pleasure to view your website! Escher has always been my favorite artist. Your efforts are an inspiration to all of us at Lawrence Berkeley National Laboratory in the USA!|
|Bill Courtney||2002-07-31 19:57:34+00|
|Brilliant and beautiful (and quite instructive). The loop and the straightened loop are fascinating to watch, and between them an understanding of the print and a glimpse of Escher's genius is made available. Thank you.|
|Martin Hollis||2002-07-31 18:01:40+00|
|A wonderful piece of work, and I'm confident Escher would have been totally enthralled. The mathematical details are a little sketchy in places, so I must ask: what exactly is the mapping between (a,b) eg (1,1) and (rotation,scale) eg (41degrees, 75%). I can't work it out in my head. And for completeness you could specify the vertical transformations fully 'the exponential map on the plane of complex numbers'.|
|Tom McCormick||2002-07-31 17:57:18+00|
|Very cool, and my (16,16,11 year-old) kids really liked the
I'm guessing that you should be able to apply the same transformations to other "infinite" pictures such as the Droste picture and the Carnation picture. I think that it would expand a lot of peoples' understanding of this to see the same thing done using a different source picture.|
|Ira Lippy||2002-07-31 16:32:37+00|
|I viewed this and other M.C. Escher pictures for years and am always amazed by them, but this has been truly awesome. I'm trying to decide if I can explain it to my twelve year old son, or just keep it to myself.|
|Fascinating work on the part of Escher and Lenstra to complete such a true joy to behold. Intuition and mathematics wonderfully complement each other in this piece.|
|Okay, the > got eaten in my post. BR
mpeg-loop -quiet -root -end 398 bclip_1_1.mpg 2> /dev/null|
|Linux users can use the application mpeg-loop (which seems to be a modified berkeley mpeg_play) that comes with electricsheep to use the mpg as a xscreensaver. just add the following as a xscreensaver program:
mpeg-loop -quiet -root -end 398 bclip_1_1.mpg 2 /dev/null
(you should use the full path to the mpg file)|
|Skip Housh||2002-07-31 14:30:41+00|
| I don't understand the math behind all this, but I love the result. Interesting to the point of fascination.
Gulf Breeze, Florida, USA|
|Mrinal Virnave||2002-07-31 14:03:55+00|
|Well Done! I never realised how complex this piece by Escher was. The wonder that is the human mind.|
Het is allemaal erg mooi geworden.
Van harte gefeliciteerd met het resultaat!
|Ian Thal||2002-07-31 13:00:00+00|
|Of course the reason Escher placed his signature in the center of "The Print Gallery" was due to the fact that it was a work that could not be finished by the means at his disposal. The picture frame that he drew spirals infinitely inward and counter clockwise and infinitely beyond the edge of the paper in a clockwise direction. The loop could only be closed by the complex techniques described on this intriguing site. What is amazing about M.C. Escher is is ability to intuitively grasp what others must measure and abstract.|
|Herb Schaaf||2002-07-31 12:26:16+00|
|Was aware of this site because of New York Times article.
Hope to return again, with hope of more understanding to
add to enjoyment. Beautiful site, well done !|
|Bernyce Byars, Ph.D., Clinical Psychologist||2002-07-31 11:09:29+00|
|Thank you for your tremendous work. Intuitively, I feel it has brought me real insight into another aspect of the human mind and, intuitively, a feeling of how it handles certain sorts of visual processing. What an outstanding accomplishment your very talented team of investigators has achieved!
Bernyce Byars, Ph.D.,
9945 Big Horn Street,
Ventura, California, USA|
|Marco Mesturino||2002-07-31 09:59:39+00|
|Joshua E. Barnes||2002-07-31 05:53:53+00|
|Great work, and a splended presentation. I'd like to see a version of
the animation with a straight zoom of the filled-in image,in addition
to the combination of zoom and rotation which you offer now.
I realize that the rotation makes the animation periodic (in the sense
that the final frame is identical to the initial frame). But I think an un-
rotated version, perhaps continued through several cycles, might give
a better understanding of the transformation underlying the ... read more|
|Audra Buchanan||2002-07-31 03:49:20+00|
|Like many others here, I also followed a link from the New York Times. Outstanding work on a most trivial piece... I hope to see more like it in the future. (Especially interactive screen savers!) ;) Keep up the extraordinary work. Regards, AB|
|Michael Richards||2002-07-31 03:49:07+00|
Have you considered applying this or similar concepts to spaces described by Riemann geometry (such as spheres) to produce unique projections of the surface of the earth; or to mobius strips and klein bottles (also favorites of Escher)?|
|Hume Smith||2002-07-31 03:41:16+00|
|Ach, now I understand this picture. With the hole, I was missing it. Thank you.|
|Matt Levin||2002-07-31 03:36:56+00|
|neat examination of escher's work. amazing that his mind was able to visualize the complex plane like that. cool!|
|Bayle Shanks||2002-07-31 03:29:46+00|
|what a wonderful work! thank you|
|C. Abrams||2002-07-31 03:09:07+00|
|Wonderful! You've extended Escher into the dimension of time. Escher found ways to tile the plane with interlocking or repeating figures; your video finds a way to 'tile' the timeline with his image. The video also reminds me of Alan Lightman's book Einstein's Dreams. Thank you so much for providing these resources - I will use them in my classes!|
|Dr. Faulkroy||2002-07-31 02:30:51+00|
|THIS IS DEFINITELY SOMETHING!
When I want non-euclidian space/time I just go to armenia, city in the sky. HTTP://UNTITLEDGIF.org/|
|Richard Morrison||2002-07-31 02:28:36+00|
That unfinished center has bothered me for years. Though not unique in this respect, it seems to conflict with M.C.E.'s own aesthetic. Your brilliant work extends M.C.E.'s great work and affords new ways of appreciating it. As Mr de Rijk's comments in the Times suggest, M.C.E. would also be thrilled. Your solution's complexity and elegance makes his ineffable genius even more awesome and compelling. So, what's next?|
|Fenix VonDiakonov||2002-07-31 01:52:36+00|
|This project is a fascinating example for hyperdimensional artists to experiment with the elusive concept of unorthodox perception.
I look forward to experiencing more artists' flirtation with the connections between art and math.
|Jonathan Gevaryahu||2002-07-31 01:50:31+00|
|This work is absolutely amazing. It shows the amazing genius that Escher was to make art like this without the assistance of a computer. Wonderful work, and thank you for sharing it!|
|BERT PARSONS||2002-07-31 01:27:52+00|
|THIS MATERIAL IS MIND BOGGLING.FOR ME A NEW INCITE INTO
THE JOINING OF MATHEMATICS AND ART.|
|Jan Rines||2002-07-31 01:27:41+00|
|Folks, you had a personal computer to make, and manipulate the graphic grid upon which to overlay/distort the image. How did Escher do it by hand? How do you make something like that?|
|Kelly Westbrooks||2002-07-31 01:25:53+00|
| -I dropped like 3 hits of acid and watched the avi....ohhh myyyyy godddddddddddddddddddddddddddddddddddddddddddddddddddddddddd dddddddddddddddddddddddddddddddddddddddddddddddddd|
|Lewis H. Homer, III||2002-07-31 00:59:44+00|
|Thank you from the great grandson of the first international president of the International Brotherhood of Teamsters, Draymen and Railyard Workers: Warren Augustus "War" Rang, a Dutchman whose daughter Miriam met my grandfather Harold Rees at Ohio University in Athens, Ohio. This e-mail from the law library one of his sons-in-law helped start in Pasco County, Florida, overseen by an Inn of Court named after the son-in-law whose daughter married Kenneth Ray Misemer, a dutch-american from Springfield, Missouri, who attended law school with me. Also, thanks to Andy Weil, Ph. D., as well as the late Prof. Fermat.|
|This site was listed with an article appearing in todays (073002) issue of the New York Times.
Wonderful site. Facinating artist. Thanks you.|
|marcus greene||2002-07-31 00:19:45+00|
|I'm an artist and math dilettante, and I agree with all the others who've responded; this is brilliant. If you keep a list of contacts please add me to it. After August 13 make it to mgreene@NHIA.edu. Thank you for sharing.|
|simon green||2002-07-31 00:05:15+00|
|a thoroughly interesting site: thank you. I followed a link from the New York Times|
|David P. Condon||2002-07-30 23:30:29+00|
|I thought that was a very interesting process to "decode" or replicate M.C. Escher's drawings.
The animation was very good. If you have not thought of it already, perhaps you could market it as a screen saver.
All the best,
|Alexa van der Waall||2002-07-30 23:27:09+00|
|Gefeliciteerd met deze prachtige site.
Het is een genoegen om naar de filmpjes te kijken.
Ze illustreren goed hoe de "Print Gallery" in elkaar steekt.
|Katie Rugh||2002-07-30 22:37:49+00|
|It is incredible. Not two days ago, my husband was remarking upon this very print, saying he wished it had been completed. He spent the entire night staring at it, ruminating. And you have completed it. Remarkable, lovely, and absolutely brilliant. I congratulate you.|
|Troy Jackson||2002-07-30 22:26:36+00|
|Thanks for making this so accessible! I enjoyed the write-up and the results tremendously. This adds another flavor to this print and made me appreciate it all the more. Thanks again. I find the animation stunning!|
|Fernando Machado||2002-07-30 21:46:48+00|
It makes Escher's work even more intriguing
Indeed, publish the software, please!|