Escher and the Droste effect
Back in February I published the post "DROSTE EFFECT"
( watch>> https://plus.google.com/+annaritaruberto/posts/Gei5xfyqZUx
), in which I informed you of what it was. Among the various links that I signaled in that post there was this:
► "The mathematics behind the Droste effect">>http://www.josleys.com/article_show.php?id=82Article’s abstract
: An image transformation method, first used by the artist M.C. Escher, and described by Lenstra et al. is generalized for use in a graphics program.
► Read too the article by B. de Smit
and H. W. Lenstra Jr.
in the pdf document “Artful Mathematics: The Heritage of M. C. Escher - Celebrating Mathematics Awareness Month”>>http://www.ams.org/notices/200304/fea-escher.pdfThis is an excerpt
:In 1956 the Dutch graphic artist Maurits Cornelis Escher (1898–1972) made an unusual lithograph with the title Prentententoonstelling. It shows a young man standing in an exhibition gallery, viewing a print of a Mediterranean seaport. As his eyes follow the quayside buildings shown on the print from left to right and then down, he discovers among them the very same gallery in which he is standing. A circular white patch in the middle of the lithograph contains Escher’s monogram and signature.What is the mathematics behind Prentententoonstelling?Is there a more satisfactory way of filling in the central white hole? We shall see that the lithograph can be viewed as drawn on a certain elliptic curve over the field of complex numbers and deduce that an idealized version of the picture repeats itself in the middle. More precisely, it contains a copy of itself, rotated clockwise by 157.6255960832. . . degrees and scaled down by a factor of 22.5836845286. . . .
In recognition of the 2003 Mathematics Awareness Month theme “Mathematics and Art”, the mentioned article brings together three different pieces about intersections between mathematics and the artwork of M. C. Escher.B. de Smit and H. W. Lenstra Jr.
are at the Mathematisch Instituut, Universiteit Leiden, the Netherlands. H. W. Lenstra also holds a position at the University of California, Berkeley.
Their email addresses are email@example.com
► Visit the website “Escher and the Droste effect”
, which aims to visualize the mathematical structure behind Escher's Print Gallery
► Watch "Print Gallery">>http://escherdroste.math.leidenuniv.nl/index.php?menu=escher&sub=orig
► Gif source >>http://pages.uoregon.edu/noeckel/computernotes/movieExample/#mathematics #droste_effect #Escher #Art #recursive_painting #science #sciencesunday #scienceeveryday