CeVis
  1. Center of Complex Systems and Visualization
  2. Lehre
  3. Oberseminar

In dem regelmäßig stattfindenden Oberseminar tragen Gäste aus aller Welt über Forschungsarbeiten zu Themen vor, die mit der Arbeit von CeVis und MeVis in Verbindung stehen, und Mitarbeiter von CeVis und MeVis präsentieren ihre neusten Ergebnisse.


C(M)eVis-Oberseminar am 15.7.1998


Datum: Mittwoch, der 15.7.1998
Zeit: 11.00 Uhr
Ort: Seminarraum Mandelbrot
Referent: Prof. Dr. A. Barbe (Katholische Universität Leuven)
SYMMETRIC COVERINGS OF TRIANGLES WITH PASCAL'S TRIANGLES MODULO 2

A Binary Difference Pattern (BDP) is a pattern obtained by covering an equilateral triangle by black and white equally sized circles in dense hexagonal packing under a simple symmetric local configuration rule. These patterns are isomorphic to certain compositions of the Pascal's Triangle modulo 2. Analytic conditions for certain types of geometrical symmetry of these patterns will be presented, and these allow to find all symmetric solutions and the cardinalities of the different symmetry classes. Edge-fitting BDP-coverings of some polyhedral surfaces with equilateral triangular faces will also be considered. In the analysis, a central role is played by the so-called Pascal Matrix -a square matrix that contains Pascal's Triangle modulo 2- and by certain groups of geometrical transformations of this matrix, featuring remarkable product properties for the Pascal Matrix.


A. Rodenhausen, 2. Juli 1998