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 16.5.2001

Datum: Mittwoch, der 16.5.2000
Zeit: 11.00 Uhr s.t.
Ort: Seminarraum Mandelbrot
Referent: Prof. Dr. Andre Barbe (Katholische Universität Leuven)

Symmetric self-organization in a cellular automaton using a random Gauss-Seidel algorithm

In a proper graphical representation of the orbit of the cellular automaton that generates Pascal's triangle modulo 2, equilateral triangular patterns may appear which are invariant under 120-degree-rotations. For a triangular pattern of size N, N being the number of cells at each of its edges, these rotationally invariant solutions are generated by the fixed points of the mapping F:2^N -> 2^N, where s -> A_Ns, where A_N is an N*N-matrix featuring Pascal's triangle modulo 2. Originating from a simple model of an electronical realization of the cellular automaton that generates the rotationally invariant solutions, an iterative procedure will be presented that also converges to these solutions, at least for not too large N. It is conjectured that convergence occurs for all N. The procedure can be considered as a random version of the Gauss-Seidel procedure for finding the solution of the linear equation Ax=x in R.