http://de.evo-art.org/index.php?action=history&feed=atom&title=The_Droste-Effect_and_the_Exponential_TransformThe Droste-Effect and the Exponential Transform - Versionsgeschichte2026-04-18T14:07:06ZVersionsgeschichte dieser Seite in de_evolutionary_art_orgMediaWiki 1.27.4http://de.evo-art.org/index.php?title=The_Droste-Effect_and_the_Exponential_Transform&diff=4168&oldid=prevGbachelier: Die Seite wurde neu angelegt: „ == Reference == Bart de Smit: The Droste-Effect and the Exponential Transform. In: Bridges 2005. Pages 169–178 == DOI == == Abstract == In this …“2015-01-31T10:20:28Z<p>Die Seite wurde neu angelegt: „ == Reference == Bart de Smit: <a href="/index.php?title=The_Droste-Effect_and_the_Exponential_Transform" title="The Droste-Effect and the Exponential Transform">The Droste-Effect and the Exponential Transform</a>. In: <a href="/index.php?title=Bridges_2005" title="Bridges 2005">Bridges 2005</a>. Pages 169–178 == DOI == == Abstract == In this …“</p>
<p><b>Neue Seite</b></p><div><br />
<br />
== Reference ==<br />
Bart de Smit: [[The Droste-Effect and the Exponential Transform]]. In: [[Bridges 2005]]. Pages 169–178 <br />
<br />
== DOI ==<br />
<br />
== Abstract ==<br />
In this note we give a correspondence between three kinds of pictures. First, we consider pictures with<br />
the “Droste-effect”: a scaling symmetry. These are drawn on a plane with a special point, which is the<br />
center of the scaling symmetry. Then we use the complex exponential map to transform these pictures to<br />
doubly periodic pictures, commonly known as wallpaper pictures, which are drawn on the entire plane.<br />
By rolling up the plane according to the periods, we get pictures drawn on a compact Riemann surfaces<br />
of genus 1: donut surfaces. As an application, we show the how the notion of a “Dehn twist” on a donut<br />
gives rise to a continuous interpolation between the straight world and the curved world of Escher’s 1956<br />
lithograph Print Gallery.<br />
<br />
== Extended Abstract ==<br />
<br />
== Bibtex == <br />
<br />
== Used References ==<br />
[1] B. de Smit, Escher and the Droste-effect (website), Mathematisch Instituut, Universiteit Leiden, 2002;<br />
http://escherdroste.math.leidenuniv.nl<br />
<br />
[2] B. de Smit and H. W. Lenstra, The mathematical structure of Escher’s Print Gallery, Notices of the<br />
Amer. Math. Soc. 50 no. 4 (2003), 446–451.<br />
<br />
[3] B. Ernst, De toverspiegel van M. C. Escher, Meulenhoff, Amsterdam, 1976; English translation by<br />
John E. Brigham: The magic mirror of M. C. Escher, Ballantine Books, New York, 1976.<br />
<br />
[4] D. Schattschneider, M. C. Escher: visions of symmetry, W. H. Freeman, New york, 1990.<br />
<br />
[5] E. Th ́e, The magic of M. C. Escher, Harry N. Abrams, New York & London, 2000.<br />
<br />
[6] J. H. van Dale, Groot woordenboek der Nederlandse taal, 12th printing, Van Dale Lexicografie,<br />
Utrecht, 1992.<br />
<br />
<br />
== Links ==<br />
=== Full Text === <br />
http://archive.bridgesmathart.org/2005/bridges2005-169.pdf<br />
<br />
[[intern file]]<br />
<br />
=== Sonstige Links ===<br />
http://archive.bridgesmathart.org/2005/bridges2005-169.html</div>Gbachelier