What does the golden spiral converge to? I am looking at pictures of spirals associated with the Fibonacci sequence and the golden ratio and I am seeing several different spiral diagrams.
For example one image I saw shows the spiral with the following numbers $8, 5, 3, 2, 1, 1$.
Then another has $34, 21, 13, 8, 5, 3, 2, 1$.
So, since the Fibonacci sequence continues forever is it possible to figure out where the golden spiral converges to in an image with Fibonacci sequence of $F_n, F_{n-1}, F_{n-2}, \dots$ ?

The Fibonacci sequence usually begins $0, 1, 1, 2, 3, 5, \ldots$  with $F_0 = 0$. The sequences above are this in reverse. The second one excludes $F_1$. It seems that $F_n$ where $n < 0$ are being excluded and you are asking for the coordinates of the the start of the spiral at $F_1$. That depends on the diagram, and the coordinate system. In general, the coordinates can be found.
