Universität Paderborn » SFB 901 » Events


Talk given by Prof. Dr. Jürgen Richter-Gebert (Technische Universität München)

Begin: Tue, 20. of Nov 2012 ( 4:00 PM)
Location: Warburger Str. 100, Lecture Hall O1

On November 20, 2012, Prof. Dr. Jürgen Richter-Gebert will give a talk about "Ornaments, Symmetry and Algorithms" in the context of the SFB 901 colloquium.


Ornaments are an omnipresent part of human culture and form intriguing objects connecting art and science. This talk focuses on plane ornaments. They are characterized by the fact that they have translational symmetries in two different directions. Such plane ornaments may be very as simple like a checker board pattern or intriguing like the well known fish/bird tesselations of the dutch artist M.C.Escher. It is known since the 19th century that there are only 17 structurally different symmetry types of such ornaments: the plane crystallographic groups. This talk focuses on various algorithmic issues related to such ornaments and their underlying symmetry groups.

- How to recognize the symmetry type of an ornament from a photo?
- How to write tools that allow people to create ornaments?
- How to algorithmically transform an ornament into other types of geometry (for instance hyperbolic or spherical geometry) while keeping its artistic content.

The talk will also include several software demos. Among them a program that is capable of transforming a planar euclidean ornament into a hyperbolic one is shown (thereby creating images that are similar to Eschers famous Circle Limit pictures). This program will utilize very recent methods from the field of "discrete differential geometry". Furthermore the talk includes a demo of the iOS app "iOrnament" which is a touch-based program for the generation of ornaments that also can be used in educational scenarios.