Fibonacci Quasicrystal Diffraction

Penrose-like 2D quasicrystal via cut-and-project; 10-fold diffraction symmetry

Real space (atom positions)
Diffraction pattern |S(q)|²
Atoms: 0 Golden ratio φ: 1.6180… Symmetry: 10-fold
About: A quasicrystal is generated via the cut-and-project method: project a 5D hypercubic lattice onto 2D using the golden ratio φ=(1+√5)/2. The resulting point set has long-range order but no translational periodicity, exhibiting 10-fold rotational symmetry forbidden for crystals. The diffraction pattern |S(q)|² reveals sharp Bragg-like peaks arranged with perfect 10-fold symmetry — exactly what Shechtman observed in 1982, earning the 2011 Nobel Prize.