On Sun, May 13, 2012 at 12:35 PM, Dan Asimov <dasimov@earthlink.net> wrote:
Mike, your images are very nice.
Thanks!
Print Gallery is my favorite of all Escher drawings, and the only one I have a print of (since 1973, even). I've been known to call it a "reality manifold" since locally (though not globally) it's realistic, just as a manifold can be locally but not globally Euclidean.
(Or like integrating f(z) = 1/z on C, which is possible in an open set not surrounding the origin, but not in one that does.)
But I've never believed that it's related to complex variables in the way claimed in < http://www.ams.org/notices/200304/fea-escher.pdf >.
Well, Escher certainly didn't think of it that way; he got the conformal map through aesthetic considerations. One "Print Gallery"-like picture I want to do would begin with "Ascending and Descending", then create a "Droste effect" by inserting a scaled-down copy of the building into the open patio around which they're walking, repeating ad infinitum. By centering on the limit point, I can then apply the conformal transformation and turn the impossible circular staircase into an even-more-impossible tower of Babel with an infinite spiral staircase and monks that grow and shrink. -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com