Escher and the Droste effect


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2004 messages since July 30 20021 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41
Page 40 of 41 (new to old)

Mike 2002-08-01 05:23:14+02
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 21:57:34+02
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 20:01:40+02
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 19:57:18+02
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 18:32:37+02
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 17:38:36+02
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 16:40:00+02
Okay, the > got eaten in my post. BR mpeg-loop -quiet -root -end 398 bclip_1_1.mpg 2> /dev/null

Maarten2002-07-31 16:38:00+02
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 16:30:41+02
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 16:03:55+02
Well Done! I never realised how complex this piece by Escher was. The wonder that is the human mind.

Joost2002-07-31 15:36:32+02
Hoi Bart, Het is allemaal erg mooi geworden. Van harte gefeliciteerd met het resultaat! Groeten, Joost

Ian Thal2002-07-31 15:00:00+02
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 14:26:16+02
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 13:09:29+02
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 11:59:39+02
Gorgeous! Thank you.

Joshua E. Barnes2002-07-31 07:53:53+02
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 05:49:20+02
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 05:49:07+02
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 05:41:16+02
Ach, now I understand this picture. With the hole, I was missing it. Thank you.

Matt Levin2002-07-31 05:36:56+02
neat examination of escher's work. amazing that his mind was able to visualize the complex plane like that. cool!

Bayle Shanks2002-07-31 05:29:46+02
what a wonderful work! thank you

C. Abrams2002-07-31 05:09:07+02
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 04:30:51+02
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 04:28:36+02
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 03:52:36+02
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 03:50:31+02
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 03:27:52+02

Jan Rines2002-07-31 03:27:41+02
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 03:25:53+02
-I dropped like 3 hits of acid and watched the avi....ohhh myyyyy godddddddddddddddddddddddddddddddddddddddddddddddddddddddddd dddddddddddddddddddddddddddddddddddddddddddddddddd

Lewis H. Homer, III2002-07-31 02:59:44+02
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 02:31:28+02
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 02:19:45+02
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 02:05:15+02
a thoroughly interesting site: thank you. I followed a link from the New York Times

David P. Condon2002-07-31 01:30:29+02
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 Waall2002-07-31 01:27:09+02
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.

Katie Rugh2002-07-31 00:37:49+02
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 Jackson2002-07-31 00:26:36+02
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 Machado2002-07-30 23:46:48+02
Incredible! It makes Escher's work even more intriguing Indeed, publish the software, please!

Steve Demeter2002-07-30 23:15:51+02
would you be interested in publicizing either a standalone program or a graphics plugin (for programs like photoshop) that works on similar end-user created images, according to this algorithm?

Martha Grenon2002-07-30 22:46:46+02
As a child in the USA I was fascinated by the Carnation Evaporated Milk can. The can had a picture of a cow on a can into infinity, and I would try to "see" how many I could count. As a grown-up I became fascinated by the work of MC Escher and always wondered why he left the middle of that drawing unfinished. Thank you for figuring it out-it's really mind-boggling!

Julie Pietrzak2002-07-30 21:44:18+02
Incredible work here. I thoroughly enjoyed your interpretation and break-down of Escher's work. Including the grids makes it all so clear. Wow. ~JAP

jp2002-07-30 21:41:49+02
Outstanding! When can we buy the print?

Jon Sjogren2002-07-30 20:59:06+02
Please inform when we can obtain screen saver version. Many would gladly pay Euros 10 Best js

Phil Carmody2002-07-30 20:55:54+02
Until today, that image was never one of my favourite Escher pieces. However, simply seeing his preparatory grid opened my eyes to the devious genius in the work. My view of it was flipped on its head. This new mathematical and artistic development is truly worthy to follow after such a piece, the two complement each other perfectly. Phil

Robert F. Kauffmann2002-07-30 20:15:27+02
As a lifetime student of Escher, I found this work to be the most impressive I've seen yet on this subject. No one has ever followed up properly on Escher's work until recently. To that end, I think you may find the following website of interest: regards, RK

Kevin McCarthy2002-07-30 16:51:08+02
I am highly impressed. Your work here is outstanding. I would enjoy seeing these techniques applied to other prints of Escher. This site is a fantastic teaching resource.

maarten de boer2002-07-30 15:21:47+02
Wow! Indrukwekkend! En duidelijk uitgelegd. Zeg, zouden jullie het Droste plaatje ook zo kunnen renderen, ter illustratie? Als ik de mpg filmpjes afspeel met mplayer -loop, dan wordt tussen de loops in het window even gesloten. Weten jullie daar iets op? Maarten

Ray Quenneville2002-07-30 14:47:36+02
Yum, a delicious mix of art and math. When will we have the screen-saver version? ;-)

Francis Perey2002-07-30 14:23:55+02
Congratulations on making a very sophisticated subject quite clear. I am missing a link to a web site where those of us have some mathematical knowledge but are not "expert" could go a little deeper into the mapping

Mitchell Cotter2002-07-30 10:48:53+02
Fascinating. The self similarity is another example of a fractal process. The relationship of these drawings to the discrete fractal processes is very interesting. I would encourage you all to pursue further examples. I will have to try playing it on some other system to make the animation work.