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|Could this effect be used to illustrate the interactions of many layers of magnification, some "layers" might include: subatomic, atomic, chemical, DNA, cellular, microbes, eukaryotic microorganisms (parasites, intermediate size), macroscopic. It could also "expand" in scientific layers to include the Universe. Just a thought.|
|Rob van Gerwen||2009-12-16 13:12:03|
|Mooi gedaan en zeer verhelderend.
Het Droste-effect is niet alleen een wiskundig probleem, maar allereerst een conceptueel probleem. Wat het Droste-effect ons laat zien is dat een afbeelding niet zichzelf kan afbeelden.
Dat is ook een filosofische analyse waardig.
Een beschrijving kan nl. wel zichzelf beschrijven:
"Deze zin bevat zes woorden."
"Deze zin is waar."
En: "Deze zin is onwaar."
Dat taal dit kan heeft te maken met haar arbitrariteit, en met het feit dat ze indexicals kent, woorden die verwijzen naar de omstandigheden van de uitspraak, zoals "ik", "deze", enz.
Afbeeldingen betekenen niet op arbitraire wijze, en ze kunnen niet naar zichzelf verwijzen.|
|Piet Smits||2009-12-16 08:27:04|
|fantastisch mooi om dit zo te zien.
ik ben escher liefhebber.
dankzij een artikel in de nrc over hendrik lenstra kom ik op deze site
ze verdient meer aandacht!!|
|geraldine de fijter||2009-12-12 16:08:14|
|l have been trying 30 min. l hate you|
|geraldine de fijter||2009-12-12 16:07:34|
|l am interested in grafic design and especially the droste chocolate box|
|Aryan Shahabian||2009-11-27 01:32:41|
|For me as an architect & a designer, geometrically & at the same time aesthetically analysing Escher's works had been a real challenge. These days I'm engaged with a postgraduate program of urbanism called "Brain City Lab" & during my studies about the geometery of brain, I found that in some cases the geometery of Riemann surfaces are related to the topic. Searching in Wikipedia about these surfaces I encountered this PDF file from Notices of the AMS that encludes very practical, important & critical alalysis of grids, methodology & etc.
This is to thank the authors for their perfect reasearch...|
|I think that what it is most interesting is that Escher decided to put that empty spot in the middle of his work.. i think that's brilliant! If he hadn't done it we wouldn't be talking about it.
He wanted to make us think.. and that's why I admire him so much.
Verónica (from Argentina)|
|jack leeder||2009-10-07 01:05:58|
|Wow very very very cool!
I felt like Alice tumbling through the looking glass.
I have studied the print gallery lithograph many times and it blew me away seeing your reworkings. most wonderful.
The masterful MC Escher has always been a great inspiration to me.
Check out my own work on FlickR (flickr.com/photos/jackleeder) and my own website, (jackleeder.co.uk)|
|vicky van Hees Martin||2009-10-03 01:24:58|
|Garamvölgyi Attila||2009-09-27 18:31:21|
|This process is very-very...nagyszerű látni, hogy milyen csodálatos lehetőségek rejlenek lényünk és a világ kapcsolatában! Lenyűgöző az a szépség, amely összeköt nézőpontokat, gondolatokat, s az alkotás gyönyörű rímeit találja látszólag messzi tárgyak kalandjai között feszülni.
Köszönet és Gratuláció a remek munkákért!!!|
|Richard Thompson||2009-09-06 19:55:24|
|Awesome. Where can I get a print?|
|E. Perez||2009-08-21 20:18:28|
|Escher was wonderful! His work shows that it takes a genius to create and mathematicians to decipher. See more about conformal mappings at 4DLab.info.|
|James Clint Lucas||2009-08-21 03:12:21|
|.....M C Escher has very little over much of my work.....I can put my money where my mouth is.....check it out
that ia lower case"L",not a one
James Clint Lucas|
|Sun Yu||2009-07-09 16:42:55|
|Hi, I'm a Chinese student and I want to learn this method very much...is there a way to make pictures like that?|
|Duilio Carpitella||2009-07-08 11:54:05|
|I wish to copy on CD the zooming image of Escher's "Gallery" for my students.
How is it possible to do? (WINDOWS XP)|
|This is a Very nice site! I just saw Portland Art Museum exhibit in Oregon. I was transfixed by Angels& Demons tesselation/fractalization draft.|
|So where do we download the program you used to create the pictures? I'm sorry but I couldn't find it.
Is it some sort of Photoshop plugin? Or is it a just program that produces JPEGs with the parameters you entered?
|Connie Voight||2009-05-22 20:06:14|
|I was most pleased to find this website as I am teaching my 5th and 6th grade students to draw with distorted grids and using Print Gallery as a model. I had the pleasure of Hendrik's company in Berkeley at my son, John's, graduation dinner. My best wishes to him and many thanks for this excellent site.|
|Paul Bodoni||2009-05-15 14:18:05|
|Mycket Bra! Äntligen! Ska Mejla Det Här Till Min Syster, Som En Gĺng I Tiden Introducerade Mig I Eschers Värld... MVH Paul Bodoni|
|Michael Peter Rolnecki||2009-04-26 16:16:32|
|This is a most interesting site, I have always loved the art and science of a man that was a gentle soul the world has treated with repect.|
|Gustavo Alkindar Brandâo Maia||2009-04-03 18:33:03|
|Parece que Escher năo teve grandes estudos de Matemática, particularmente de Topologia. O que reforça o pensa,mento de Einstein: "A imaginaçăo vale mais que o conhecimento".
Uso frequentemente os trabalhos de Escher nas minhas aulas.|
|Tos Berendschot||2009-03-27 13:18:16|
|Some time ago I watched the paradiso lecture on the effect by Prof Lenstra. It has long been in archive online, but I cannot find it anymore.
I would like to watch the lecture ones more with my son.
Is there a possibility??
with regards, Tos Berendschot|
|Constantino Landa||2009-03-12 17:22:31|
|Excelent!! I am an Industrial Designer teaching in Mexico City and have been using your work for about 2 years. It is a great way to understand patterns and geometry in a practical exercise. Thank you very much!|
|Hans Krol||2009-02-24 11:23:16|
|Interesting site honouring the excellent artist M.C.Escher.
Hans Krol (Heemstede)|
|Bryan Kaye||2009-02-20 07:39:28|
|An artistic expression of mathematics...I like it!|
|Richard R.||2009-02-18 22:09:36|
|Fascinating! Art and science unite? Can it be?|
|Henry Droste||2009-02-14 21:30:16|
|Awesome! This is EXACTLY what I needed for my geometry paper, I was told to research Escher and the mathematics of his art, and this just fits the bill!|
|ian kupczyk||2009-02-09 00:40:46|
|Thx for sharing such a fascinating story|
|guido mittiga||2009-02-06 09:54:58|
|the numer one of droste effect!|
|Nice work. This is a great explanation, and helped 100% on my math paper (summary of the math in Print Gallery). Greatly appreciated, and once again, GREAT JOB!|
|Kelly DeGon||2009-02-03 00:53:36|
|This is such a great project! I want to thank you for sharing your work. I find it fascinating that Escher is able intuitively adapt to this level of mathematics.|
|kimberly turner||2009-01-25 19:16:00|
|Johanna Nordgaard||2009-01-23 13:18:39|
I have just finished a BSc in product development and design, and during that have I been teaching in art and working with graphic design in a local newspaper. Today I found the main connection between my creative search. To work between the magic and logic, and that made me very happy! I am a big fan of Escher. Thank you for your excellent work with this website.|
|Emilio Turbay||2009-01-18 04:19:19|
|Escher one of my heroes of the greatness of the human brain.|
|Carlos M. Morel||2009-01-15 11:11:55|
|Excellent site, congratulations!
Carlos M Morel
Rio de Janeiro, RJ, Brazil|
|Are we self-referenced objects?|
|That was cool! I loved seeing the animations and how to generate different grids like the one escher used, as well as your explanation of why there's a blotch missing: because that blotch would contain a smaller version of the entire|
|Hi, im brittany and i just wanted to sy that i loved your work and that im an artist myself and that i hope to oneday be as good as you.|
|Nikolaos Petrakakis||2008-11-23 09:18:36|
|Thank you for a very decent approach, to math art culture.|
|great job. A really interesting retrospective to Escher's work.
|Stephen M. Hunt||2008-11-12 12:48:24|
|I thought you might like to know about my play Impossible Steps inspired by Escher's Ascending & Descending. Further info is available at our website, I'd be happy to advise you its details. This play had a three week run at the Rosemary Branch Theatre, London 6 weeks ago. I am planning other UK productions as well as a tour of Holland where I hope to put on the play at Escher's Arnhem school which is said to be his inspiration for Ascending & Descending.|
|Stephen M. Hunt||2008-11-12 12:45:11|
|I thought you might like to know about my play Impossible Steps inspired by Escher's Ascending & Descending - for further info go to www.impossiblesteps.webeden.co.uk This play had a three week run at the Rosemary Branch Theatre, London 6 weeks ago. I am planning other UK productions, as well as a tour of Holland where I hope to put on the play at Escher's Arnhem school which is said to be his inspiration for Ascending & Descending.
Please let me know if a reciprocal link between our sites is of interest to you. Best wishes, Stephen|
|Thomas Barkow||2008-11-12 05:58:36|
|Prof. Stefenhagen's presentation in Cologne was 10 times better and more coherent and a hundred times more witty than the web-presentation here.
For centuries mathmatics lacked of comprehensibility (and often avoided to have) but since two or three decades some protagonists respect understandability.
One of them ist Stefenhagen.
Thank you, Peter.|
|Thanks for explaining the whole procedure so well that I was actually able to understand it!
Those animations made my head dizzy!