Escher and the Droste effect

 

Reinko2010-03-30 20:17:18
This evening (30 March 2010) I visited a public lecture (the so called Bernoulli lezing in Groningen) given by Mr. Lenstra. In the lecture Lenstra explained a bit of the math used, most boiled down to taking the log of a picture and 'store' that in the computer. (This is not that difficult, you go from rectangular to polar coordinates and apply the complex log. A piece of cake.) But you can also create easily a picture with eight of those disappearing points, think for example an octopus holding in each of it's 8 arms a tray with a Droste package. The Droste picture has only one disappearing point that you can magnify to get the original back... Now, about one hour after the lecture, I think the answer is obvious: If you have eight of those points you can use the Riemann surface associated with the log to wrap your picture on. You must stretch your picture of course but if you do it properly you can take the log of the picture (you get a complex number by doing so). So it was a pleasant evening, the lecture was nice, the weather was not horrible and the beer was boring.