Strictly local self-assembly algorithm for a quasiperiodic octagonal tiling

Ilya Galanov
LIPN, Univ. Paris 13
https://lipn.univ-paris13.fr/~galanov/

Date(s) : 24/09/2021 iCal
11h00 - 12h30

Self-assembly is the process in which the components of a system, whether molecules, polymers, or macroscopic particles, are organized into ordered structures as a result of local interactions between the components themselves, without exterior guidance. This talk is devoted to the self-assembly of aperiodic tilings. Aperiodic tilings serve as a mathematical model for quasicrystals – crystals that do not have any translational symmetry. Because of the specific atomic arrangement of these crystals, the question of how they grow remains open. Simulations strongly support the evidence that the algorithm we developed grows aperiodic cut-and-project tilings with local rules up to an unavoidable but neglectable proportion of missing tiles. In this talk, we state the first theorem regarding the Golden-Octagonal tilings and formulate conjectures for future results.
https://lipn.univ-paris13.fr/~fernique/etudiants/ilya_these.pdf