Some unpublished notes of Hofstadter
A copy of Hofstadter's paper is on OEIS here: Link to Eta-Lore paper
It is also referenced on OEIS at A001468.
This graph is looks like a graf of the function which replaces partial quotient (in nearest integer continued fraction) in the following way: $$a_i+~\leftrightarrow~a_i+1-.$$
For example
$$0+\cfrac{1}{3-\cfrac{1}{4+\cfrac{1}{5+0}}}\leftrightarrow
1-\cfrac{1}{2+\cfrac{1}{5-\cfrac{1}{6-0}}}.
$$
\begin{align*}
\frac{1}{2}=\frac{1}{2+0}&\leftrightarrow1-\frac{1}{3-0}=\frac{2}{3},&\frac{1}{3}=\frac{1}{3+0}&\leftrightarrow1-\frac{1}{4-0}=\frac{3}{4},\\
\frac{2}{5}=\frac{1}{2+\frac{1}{2+0}}&\leftrightarrow1-\frac{1}{3-\frac{1}{3-0}}=\frac{5}{8},&\frac{3}{5}=1-\frac{1}{2+\frac{1}{2+0}}&\leftrightarrow
0+\frac{1}{3-\frac{1}{3-0}}=\frac{3}{8}.
\end{align*}
The picture from the book:
