Escher and the Droste effect


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Frances de Vries2012-10-16 23:50:31
Captivating artistry! Intriguing engineering feats with an artist flair. I have just discovered you thru my 20 year old daughter Anna! Do you have a biography in print?

Jackie Aldridge2012-10-16 18:17:58
Thanks for the interesting site. jackie

Jose Luis2012-09-15 21:52:04
Thanks for the site. It is always nice to revisit M.C.Escher, and specially the mathematics associated with his work.

knezmej2012-08-06 11:12:54
Thank You

Joe Corneli2012-07-24 04:32:44
Inspiring even many years after the fact - maybe my favorite Esher drawing.

Irene Thompson2012-07-19 19:09:37
Comin' atcha from California. Loved your site.

bobo2012-07-08 20:39:13
wish that this was easier to grasp..

Lloyd Smith2012-06-07 14:56:13
Wonderful insights!

Luna2012-04-22 00:55:12
This is great information for my research paper, thank you so much!

Chris Strunz2012-03-06 07:55:57
Wow. His art is amazing. It's so complex.

Jessica Rojo2012-02-22 16:38:05
Very nice!

Sophie2012-02-15 16:05:47
Really great site and plenty of information, I could watch Escher artworks for hours and read about his way to distord images for hours too. Thanks for your work here :)

John Walker2012-01-03 06:34:34
Escher has always been my favorite artist. His prospective and logic are fascinating. He has influenced my art, photography, and has allowed me to 'see' beyond what is in front of me.

Richard Juday, PhD2011-12-11 05:21:49
Very nifty mathematical explanation of what Escher was doing almost solely intuitively. What a pleasure to run across this site! I have been doing some related work, in which source images are filtered random fields and rendered in color. I have some new things to try now!

Sebastián Osorio2011-11-19 15:34:47
Great exposition @Universidad de los Andes. I have a new perspective of Escher's Work. Thanks a lot.

Holden Madick2011-11-16 00:03:30
Great website! Loved the fascinating patterns displayed! Helped me greatly on my art history report.

Shelender kumar2011-10-26 09:03:59

richard harding2011-10-24 02:28:20
Thank you. I stumbled on this site as I was reading the book "Godel, Escher, Bach", by Douglas Hofstadter. Your site elaborates in greater detail some of the concepts in his book. Your website is wonderful! Thanks again!

Angela Maria Camara Nogueira da Gama2011-10-02 15:38:12
É incrível o talento de Escher e arrebatador. Foi para mim o precursor da ideia de sustentabilidade, no moto contínuo que materializou, onde a energia potencial da água em queda se transforma em mecênica da roda d'água, criando um movimento infinito sem consumo energético. Um matemático que desenha, um desenhista que calcula. Gostaria de ter conhecido de perto seu processo criativo!

Roger J. Tremblay, PhD2011-09-24 16:13:22
Inspirational example of how a complex but beautiful application of mathematics can be presented with such clarity. I have never seen anything quite like it, web, television, text or live presentation (should be presented at TED?). Thank you for your efforts.

Julle2011-09-20 16:10:45
Thank you for the interesting site! Spooky mathematics, luckily you have the stop button.

Drs. Albert Spijkers2011-08-14 14:27:00
I always liked Droste Chocolate, but makes you fat. But al fun aside, I had a book once about Escher explained, but WebGL can do a much better job explaining Escher's Lithographs. Infinitely moving down in the drawing details, like with fractals.

wayne ferguson2011-08-09 00:55:05
i am looking for the mantis

Baumann Eduard2011-07-20 16:05:52
Nice, this infinity with the limited AVI file.

Marcia Weinhold2011-07-07 22:18:45
Thank you! This is fascinating!

Ryan-Georgia2011-07-06 08:35:29
Great site! Escher is one of my favorite artists ever, and you did a great job explaining the mathematics behind the art.

paul2011-06-28 00:50:55
Brilliant...on both Escher's and Lenstra's part... It is so interesting to see mathematical and artistic intuition cross-fertilizing. Grand unification of art and math - rather than GUT in physics. Escher/Lenstra personificaton of intuitive mathematician/artist. Always been fascinated by Hofstaeders book - Goedel, Escher, Bach and somehow this analysis kills the notion of incompleteness of Escher.

Cathy - Pittsburgh2011-05-02 15:54:44
As perfect a blend of art, imagination and mathematics as I've ever seen: a genius' work! ☺

Bill Hackborn2011-04-16 00:38:50
Great site! Very interesting.

Aaron2011-04-07 01:15:51
Thank you very much for sharing your work at Grinnell College. Your presentation was extremely interesting and entertaining.

Esha2011-04-05 22:18:23
Hello, Glad to see fellow Escher enthusiasts, I have been curious about him for many years now, and as the days go by, my curiosity increases, I cant wait to see what you come up with next!

Chris Miller2011-04-04 20:29:02
This is a very interesting topic. I had always wondered about the "scotoma" in " the Picture Gallery".

Aditya TVM2011-03-05 06:25:21
Thanks a lot, if not for this site, i wouldn't have know the existence of Escher-Droste effect(i accidentally came across this site) and the whole process of how this genius artist made his awesome artwork... :) i will try sketching with the reference to Escher's graph... thanks to your step by step detail description and examples:) Thanks again... :)

Hans Wassink2011-02-20 09:06:05
Of all the ways man can spend his time, this is by far the best. Keep it up! :D

Anton Älgmyr2011-01-23 00:43:16
Thanks for the great lecture at the Sonja Kowalevsky days! It was by far the most interesting one we heard in the whole weekend (the participant's survey confirms that as well)! I doubt you remember this, but I was the one who couldn't resist giving you a thumbs-up when I saw you just after the lecture. ;) Take care!

Carla Blankevoort2011-01-05 18:41:39
What a genius and wonderful that his genius lives on through this site and has other young geniuses working out his methodology! I wish I was clever enough to work it out myself, well done!

piet2010-11-28 10:03:55
escher is een flut schilder.

Dr. Tom C.J. Gribnau2010-11-14 11:21:14
Excellent work rding an excellent "artist"

Gustav Jonsson-Glans2010-11-13 23:39:16
Great lecture at the Sonja Kowalesky days! Was really fascinating and inspiring, I'll look further into the technical aspects of this method.

Gustav Jonsson-Glans2010-11-13 23:39:00
Great lecture at the Sonja Kowalesky days! Was really fascinating and inspiring, I'll look further into the technical aspects of this method.

Jan Hus2010-11-10 22:44:25
I never heard of the Droste effect, but I vividly remember the Drosty container as a five year old. It must have been in 1933. My mother was in the hospital in Singapore and a Droste can was sitting on the table beside her bed. I think I was trying to see how far back I could still see a can. I did not remember the Droste name, but I was amazed to see the picture again. Wow the Droste effect. Thank you. Jan Hus

Judai Burton2010-10-03 14:10:34
a fascinating look into liberal arts math!

Andrew Wyszkowski2010-09-30 03:43:30
Thank you for this study. I now have to digest it. Best regards.

Fader2010-08-27 19:43:13
Beautiful stuff! ..thank you.

jock mctavish2010-08-25 03:57:54
you do him honour and extend our curiosity in the same way he first attracted us very well done thankyou

Guilan Raphaelle Gistand Runty2010-08-07 22:33:10
Uitstekend! Dank je wel! Nous pouvons exploiter les excellentes informations sur ce site, Merci pour les instructions du grand professeur de Recife (Brésil), le Prof. Dr. JOSÉ CLAUDINIER DE FREITAS FILHO. Fabulous économiste, maître, écrivain, commissaire de la Trésorerie, analyste de systèmes et spécialiste de la culture, en particulier dans le nord-est du Brésil. Guilan Raphaelle Gistand Runty – Avignon - France –

Tonya M.2010-08-02 22:57:33
On August 1, 2010, I saw this at the New Britain Museum of American Art in CT, USA. Amazing to see this animation and plenty of Escher's originals in person!

Xezlec2010-06-19 15:21:02
It would be interesting to use some version of hypercomplex numbers to do the same trick with a three-dimensional grid. Make a 3D gallery that contains itself, for instance. Anyone trying that?

Xezlec2010-06-19 15:13:56
Wonderful explanation! Thanks for this.

Cheryl2010-06-17 13:20:48
This is amazing!!!!!! Thank you for giving such a clear explanation.