## Wednesday, October 21, 2009

### Tiling, Bravais Lattice, Squiggles

This is the first successful image in a new project that grew out of my tilings project. I created the image in three steps. First, I made a non-periodic tiling. Then I generated a lattice of vertices including all potential vertices around each tile. Then I plotted a shape or lines (in this case, a squiggle) at each lattice point. The plot of vertices is somewhat like a Brazais lattice, though I'm extending this math concept for my own purposes.

Tilings of the plane using tile sets of regular polygons, rectangles, isosceles triangles, trapezoids, and parallelograms, have vertices that lie in characteristic patterns or lattices depending on the properties of the polygons — its angles and sides. The Bravias lattice system categorizes these patterns. The five Bravais lattices for two dimensions approximate the arrangement of vertices of simple periodic tilings. I'm applying this concept to complex, non-periodic tilings with large tile sets.