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| Howard Wiseman | 2004-03-19 01:52:40 |
| Impressive and fascinating almost beyond words.
However I still feel frustrated that I don't fully understand the relation between the Droste effect and Escher's picture. In the "Euclidean" version of the picture, there is a straight-forward Droste effect. Then you (following Escher) do some transformation that makes it seem like the picture contains the boy looking at that very picture (not just a smaller version of the boy looking at a still smaller version of the picture and so on). I don't understand how this is achieved. I tried reading your published article but that did not help.
I feel that the hole in the middle is critical to this. Hofstadter says the hole can be made as small as you like, but I don't I believe this anymore. Obviously you have shown (beautifully) that the hole can be filled completely, but at the "expense" of introducing an infinite recursion. It seems to me Escher knew exactly what size to make his hole. But mathematically what is it that determines this?
It would be incredibly cool, and hopefully instructive, to make an animation that slowly morphs the Euclidean picture with the Droste effect into your completed Escher picture. Then I might understand. Somehow the rectangular frame of the picture morphs so that there is a continuous line (a spiral) joining all the frames of all the pictures all the way down. I can't imagine how that can happen from a continuous transformation. Is it a continuous transformation?
I don't know if you still read these messages, but if you do, I would really appreciate a response. I am a theoretical physicist by trade, if that helps. |
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