Abstract
A random-tiling model with octagonal symmetry is presented. The tiles are the square and various hexagons. When each vertex of the tiling is decorated by a disc, a valid disc packing is formed, which is an octagonal disc packing of maximum density under certain constraints. A simple inflation rule is given that produces one member of the random-tiling ensemble. The space group of this tiling is non-symmorphic. The projection description of this tiling involves a fractal acceptance domain with fourfold symmetry for the even nodes of a four-dimensional cubic lattice and the same acceptance domain rotated by pi /4 in perpendicular space for the odd nodes. Other tilings can be generated by an inflation rule with constrained randomness. Additional members of the random-tiling ensemble can be created from inflation-generated tilings by a set of update moves that rearrange the positions of the discs along closed loops. An update move does not always conserve the number of each kind of tile.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have