(They might not be the same when there is some point where three or more multigrid lines intersect, what de Bruijn called a “singular” multigrid. I have implemented both the cut-and-project and multigrid methods, and you can switch between them to see that they (almost) always produce exactly the same tiling. A face orientation is determined by two axes, so for an n-dimensional lattice, there are n choose 2 = n(n-1)/2 face types. All faces of the same type get the same color, and there is one type for each face orientation in the lattice. Note that when you move the view by dragging, this will also change the offset!Ĭolors: pick colors for the tiling faces. Specifically, this is the offset of the center of the tiling view relative to a nearby lattice point. Offsets: change the position of the cutting plane relative to the lattice. You can also choose the number of dimensions (number of axes) of the lattice. Each control point corresponds to one axis of the lattice.
Mouse-wheel to zoom.Īxis Controls: change the orientation of the cutting plane.
#5d hypercube generator
This tiling generator produces the tiling for any cutting plane orientation and offset, using either cut-and-project or a multigrid (generalized pentagrid).Ĭlick and drag the tiling to pan around. He also showed how this is equivalent to a method that uses 5 sets of parallel lines, which he called a pentagrid. This method, also called the projection method, was discovered by de Bruijn in his investigation of the Penrose tiling discovered by Roger Penrose.ĭe Bruijn observed that the Penrose tiling appears as the projection of a 5D square lattice when the cutting plane has a particular orientation and offset to the lattice. This applet draws plane tilings by cutting through a 3-or-more-dimensional square lattice with a 2-dimensional plane and projecting that slice of the lattice onto the cutting plane. Cut and Project Tiling | cut-and-project-tiling cut-and-project-tiling Cut-and-project tiling generator.
0 kommentar(er)
