Tag: Penrose tiling

  • de Bruijn’s pentagrids

    In a Rhombic tiling (aka a Penrose P3 tiling) we can identify five ribbons. Opposite sides of a rhomb are parallel. We may form a ribbon by attaching rhombs along opposite sides. There are five directions taken by sides, so there are five families of ribbons that do not intersect, determined by the side directions. […]

  • Penrose’s aperiodic tilings

    Around 1975 Sir Roger Penrose discovered his aperiodic P2 tilings of the plane, using only two puzzle pieces: Kites (K) and Darts (D) The inner angles of these pieces are all multiples of $36^o = \tfrac{180^o}{5}$, the short edges have length $1$, and the long edges have length $\tau = \tfrac{1+\sqrt{5}}{2}$, the golden ratio. These…

  • Conway’s musical sequences

    Before we’ll come to applications of quasicrystals to viruses it is perhaps useful to illustrate essential topics such as deflation, inflation, aperiodicity, local isomorphism and the cut-and project method in the simplest of cases, that of $1$-dimensional tilings. We want to tile the line $\mathbb{R}^1$ with two kinds of tiles, short ($S$) and ($L$) long…