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The function $f(x,y)$ gives an ordered pair as output.  It is defined according to the following rules:
* If $x > 4$, $f(x,y) = (x - 4,y)$.
* If $x \le 4$ but $y > 4$, $f(x,y) = (x,y - 4)$.
* Otherwise, $f(x,y) = (x + y + 11, x + 2y + 16)$.
 

A robot starts by moving to the point $(1,1)$.  Every time it arrives at a point $(x,y)$, it applies $f$ to that point and then moves to $f(x,y)$.  If the robot runs forever, how many different points will it visit?

 Dec 12, 2023

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