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Fractally shaped acceptance domains of quasiperiodic square-triangle tilings with dedecagonal symmetry

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Listed:
  • Baake, M.
  • Klitzing, R.
  • Schlottmann, M.

Abstract

We generate a quasiperiodic, dodecagonally symmetric tiling of the plane by squares and equilateral triangles embedded in a higher-dimensional periodic structure. Starting from a 4D lattice frequently used for the embedding of dodecagonal structures, we iteratively construct an acceptance domain (AD) for a quasiperiodic point set which proves to be the vertex set of a square-triangle tiling. It turns out that our procedure leads to fractally bounded ADs but leaves enough freedom to generate several different local isomorphism classes.

Suggested Citation

  • Baake, M. & Klitzing, R. & Schlottmann, M., 1992. "Fractally shaped acceptance domains of quasiperiodic square-triangle tilings with dedecagonal symmetry," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 191(1), pages 554-558.
    • Handle: RePEc:eee:phsmap:v:191:y:1992:i:1:p:554-558
    DOI: 10.1016/0378-4371(92)90582-B
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    1. Cahn, Anne H., 1984. "Mimicking Sisyphys: America's Countervailing Nuclear Strategy. By Louis Rene Beres. (Lexington, Mass.: D.C. Heath, 1983. Pp. xiii + 142. $19.95, cloth; $7.95, paper.)," American Political Science Review, Cambridge University Press, vol. 78(1), pages 265-265, March.
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