Non-periodic Tiles Based on Ammann Set A2 Tiles

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Chirag Mehta: Non-periodic Tiles Based on Ammann Set A2 Tiles. In: Bridges 2014. Pages 425–428



I present here three different non-periodic tile sets TS1, TS2 and TS3. Tile set TS1 is deduced from the Ammann set A2, and is a triangular version of it. TS2 is a variant of tile set TS1, while TS3and TS2 are MLD (Mutually Locally Derivable). These tiles are based on Golden Ratios Ø = 0.618034 and φ =1.618034.

Extended Abstract


Used References

[1] Penrose tiling, (as of March 16, 2014)

[2] Ammann R., Grünbaum B., Shephard G. C., Aperiodic tiles, Discrete & Computational Geometry, 8:1 (1992), 1-25.

[3] Baake M. et al., Quasiperiodic tiling with tenfold symmetry and equivalence with respect to local derivability, J. Phys. A: Math. Gen. 24, 4637 (1991).


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