Limit-quasiperiodic Ammann bars and two-dimensional limit-quasiperiodic structures

Abstract

Five octagonal limit-quasiperiodic tilings (octagonal limit-quasiperiodic lattices) are constructed with the grid method on the basis of limit-quasiperiodic Ammann bar grids. They are self-similar with scaling ratio . They belong to different locally-isomorphic classes but are mutually-locally derivable from each other. Each of them can be represented as a section of a four-dimensional limit-periodic structure with polygonal atomic surfaces.

Acknowledgments

I am grateful to N. Fujita for valuable comments on the manuscript.