Quasiperiodic tilings: a generalized grid-projection method

Quasiperiodic Tilings: A Generalized Grid–Projection Method

We generalize the grid–projection method for the construction of quasiperiodic tilings. A rather general fundamental domain of the associated higher dimensional lattice is used for the construction of the acceptance region. The arbitrariness of the fundamental domain allows for a choice which obeys all the symmetries of the lattice, which is important for the construction of tilings with a give...

Quasiperiodic tilings and SOC

Self-organized critical (SOC) models are used to describe the 1/f-spectra of rather different physical situations like snow avalanches, noise of electric currents or luminosities of stars. The prototype of the SOC-models is the sandpile model of Bak, Tang and Wiesenfeld (Phys. Rev. Lett. 59, (1987) 381). We implement this model on the 8-fold AmmannBeenker tiling where the model can become eithe...

Quasiperiodic Structures Obtained by the Projection Method

Cluster Interactions for Quasiperiodic Tilings

A cluster for the octagonal square-rhombus tiling is presented, which has the property that among all tilings completely covered by the cluster the perfectly quasiperiodic and eightfold symmetric ones have the highest cluster density. Since on these eightfold symmetric tilings there is considerable overlap of clusters, it seems likely that these tiling have the highest cluster density even amon...

Quasiperiodic Tilings Derived from a Cuboctahedron —Projection from 6D Lattice Space—

A 3D quasiperiodic tiling derived from a cuboctabedron is obtained by projection from 6D lattice space to 3D tile-space, one less dimensional lattice space than the conventional one. A lattice matrix defining projections from 6D lattice space to tileand test-space is given and its geometric properties are investigated.