This tiling generator produces the tiling for any cutting plane orientation and offset, using either cut-and-project or a multigrid (generalized pentagrid). Quick description of the controls

The ingredients for a cut and project scheme are the ‘direct space’ G, where the model set (or the tiling) lives, the internal space H H, a lattice L L in G × H G × H and a compact set W W - the …

Jun 15, 2022 · Fibonacci chain can be obtained by cut-and-project method. On the other hand, the Fibonacci chain and the CP chain share many properties, some of which are explained in …

QGR geometer and mathematician Dugan Hammock presents a brief overview of two methods for generating quasicrystals: the multi-grid method and the cut-and-project method. Each …

Team: Noah Koopman, Ingmar LowackAbstract: In 1981, N. G. de Bruijn introduced a novel method for generating Penrose tilings by projecting particular points ...

Construction in steps: Given a crystallographic tiling T of E n, cut-and-project data (K, E) for E n can be used to construct a new tiling T 0 of E through the following steps: (i) Choose point-set …

Nov 14, 2024 · Roughly speaking, a cut and project scheme takes an ‘irrational slice’ of a periodic pattern (a lattice) in a higher dimensional space, producing a structure which is no longer …

Definition: cut-and-project scheme The data (L, Rd, A) defines a cut-and-project scheme if A is a locally compact Abelian group, L is a lattice in the group Rd × A π = πRd , πint = πA natural …

A well-known method to construct aperiodic tilings (for example, the Penrose tiling) was the cut-and-project method. This method starts with a lattice in a high-dimensional space, wherein a …

The cut-and-project method is in fact equivalent to a multi-dimensional extension of the grid method [24], compare [4, Sec. 7.5.2]. We illustrate it in Figure 2 for a Fibonacci set, compare …