Escher and the Droste effect


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Page 40 of 41 (new to old)

Joseph M. Johnson2002-08-05 23:34:10+00
This site conveys the beauty of mathematics to the layman. By that, it does a service to the world community. If only we could more routinely popularize our interpretations of this most natural entity.

Vic Hirsch2002-08-05 17:17:40+00
Your site is the best use of the web I've seen in quite a long time. The animations are especially helpful. Thanks so much!

Jerome Sable2002-08-05 15:50:18+00
I have been in awe of Esher's "Print Shop" for many years. Thanks for illuminating and extending it so beautifully. I will be returning to this site many times.

George W. Hart2002-08-05 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 Peres2002-08-05 13:47:25+00
erg goed!!!

Laura Donaldson2002-08-03 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

patricia2002-08-03 15:24:08+00
RESPECT It is so wonderfull, before i've seen it I was blind.It opened my eyes so wide.Thank you

Rod McCallum2002-08-03 13:32:57+00
Wow. Who needs drugs to twist their brain? :-) Impressive. Fine work. Fine site. Well done.

Wendi Boettcher2002-08-03 00:10:10+00
P H E N O M E N A L !!! Thank-you, wendi

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. Rosenblum2002-08-01 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 r2002-08-01 21:35:32+00
Hitl: what Lincl had to have said to beget assasination

Bob Faulkner2002-08-01 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 Lehar2002-08-01 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? Steve Lehar

Arko Ghosh2002-08-01 04:06:00+00
Simply amazing!

Mike 2002-08-01 03:23:14+00
Spectacular 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 Courtney2002-07-31 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 Hollis2002-07-31 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 McCormick2002-07-31 17:57:18+00
Very cool, and my (16,16,11 year-old) kids really liked the animations. 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 Lippy2002-07-31 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.

Splohn2002-07-31 15:38:36+00
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.

mdeboer2002-07-31 14:40:00+00
Okay, the > got eaten in my post. BR mpeg-loop -quiet -root -end 398 bclip_1_1.mpg 2> /dev/null

Maarten2002-07-31 14:38:00+00
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 Housh2002-07-31 14:30:41+00
I don't understand the math behind all this, but I love the result. Interesting to the point of fascination. Thank you! Skip Housh Gulf Breeze, Florida, USA

Mrinal Virnave2002-07-31 14:03:55+00
Well Done! I never realised how complex this piece by Escher was. The wonder that is the human mind.

Joost2002-07-31 13:36:32+00
Hoi Bart, Het is allemaal erg mooi geworden. Van harte gefeliciteerd met het resultaat! Groeten, Joost

Ian Thal2002-07-31 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 Schaaf2002-07-31 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 Psychologist2002-07-31 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 Mesturino2002-07-31 09:59:39+00
Gorgeous! Thank you.

Joshua E. Barnes2002-07-31 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 Buchanan2002-07-31 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 Richards2002-07-31 03:49:07+00
Just brilliant. 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 Smith2002-07-31 03:41:16+00
Ach, now I understand this picture. With the hole, I was missing it. Thank you.

Matt Levin2002-07-31 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 Shanks2002-07-31 03:29:46+00
what a wonderful work! thank you

C. Abrams2002-07-31 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. Faulkroy2002-07-31 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://

Richard Morrison2002-07-31 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 VonDiakonov2002-07-31 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. Thank you

Jonathan Gevaryahu2002-07-31 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 PARSONS2002-07-31 01:27:52+00

Jan Rines2002-07-31 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 Westbrooks2002-07-31 01:25:53+00
-I dropped like 3 hits of acid and watched the avi....ohhh myyyyy godddddddddddddddddddddddddddddddddddddddddddddddddddddddddd dddddddddddddddddddddddddddddddddddddddddddddddddd

Lewis H. Homer, III2002-07-31 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.

Rachel2002-07-31 00:31:28+00
This site was listed with an article appearing in todays (073002) issue of the New York Times. Wonderful site. Facinating artist. Thanks you.

marcus greene2002-07-31 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 Thank you for sharing.

simon green2002-07-31 00:05:15+00
a thoroughly interesting site: thank you. I followed a link from the New York Times

David P. Condon2002-07-30 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, Dave Condon

Alexa van der Waall2002-07-30 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. Alexa.