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 12.6.2002

Datum: Mittwoch, 12. Juni 2002
Zeit: 11.00 Uhr s.t.
Ort: Seminarraum Mandelbrot
Referent: Prof. Dr. Andre Barbe (Katholische Universität Leuven)

Symmetric configurations in a cellular automaton under random feedback: additional results

Consider a top-down equilateral triangular array T of cells, each cell of which has a state in F2 such that any triple of touching cells in it which form an elementary top-down triangle satisfies the local matching condition that the sum modulo 2 of the cell-states in this elementary triangle equals 0. This is called an (F2,+)-configuration. The symmetry of this matching rule allows (F2,+)-configurations to be rotationally symmetric. A recursive procedure which establishes a randomized feedback between cell-states of the right edge in T and the top edge of T provides rotationally symmetric solutions.

In a first part, some experimentally obtained results concerning the average number of iteration steps needed for reaching a rotationally symmetric equilibrium solution in function of the size of the triangle T will be presented. In a second part, we consider the problem of characterizing generating sets. These are subsets of T such that an assignment of F2-values to the cells in these subsets are in 1-1- correspondence with the (F2,+)-configuration. These generating sets can be used in a generalized recursive feedback scheme. It will be shown that generating sets form a matroid, called the (F2,+)-Pascal matroid, which is a subset of a more general and geometrically defined matroid, the bases of which are candidates for generating sets of (G,*)-configurations when the local matching is defined by some quasigroup (G,*).