The pale curves inside the tent map's orbit diagram are not decoration — they are the successive images of the critical point, cn(s) = fsn(½). The density piles up along them because every one is a fold in the map. Here the density is held back and the curves are drawn on top, one iterate at a time.
The first two are closed forms: c1 = s/2, the straight upper envelope, and c2 = s − s²/2, which reaches zero at s = 2. After that they fold repeatedly. The vertical guides mark s = ⁴√2 and s = √2, where bands merge — note how the curves cross there.