Cluster Interactions for Quasiperiodic Tilings
نویسنده
چکیده
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 among all square-rhombus tilings. An interaction favouring the cluster therefore will have ground states which are perfectly quasiperiodic and eightfold symmetric.
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