30:T72d,# A tiling algebra Here we implement a handful of operators applied to tiles defined as a sequence of angles, assuming that all tiles have the same side length. Class **`Border`** encapsulates an arrangement of tiles and keeps track of the border of the arrangement as well as the position and orientation of the enclosed tiles. The following operators are defined: - **Join** joins two borders. The operation is implemented by stitching the first edge one border with the first edge of the other. - **Shift** rotates the circular sequence of angles. This can be used to select the edge which will be used in Join ops. - **Mirror** reverses the circular sequence of angles. The algebra can be exercised with ops and unit tiles encoded as a string, or *formula*. Here's the syntax used in the demo below: - Unit tiles used in *Archimedean* mosaics - **e** - Equilateral triangle - **q** - Square - **h** - Hexagon - **o** - Octagon - **k** - Dodecagon - Unit tiles used in *Islamic* mosaics - **t** - Tie - **b** - Bowtie - **d** - Decagon - Operators - **+** - Joins the two borders on the top of the stack - **=** - Duplicates the top of the stack - **>** - Shifts the top of the stack +n times, where n is either a number preceding the op or 1 if no number is given - **<** - Shifts the top of the stack -n times - **|** - Mirrors the top of the stack Note that ops are applied using RPN (reverse polish notation). For instance **eq+** is a square joined with a triangle. In the demo, the border is drawn in **red**. The join edge is drawn in **blue**. There is minimal error detection, but if the resulting border is self-intersecting you will (probably) see it, since the tiles are filled using a transparent color by default.

31:T89e,{ const width = 800; const height = 600; const canvas = htl.html`