This is a 2-dimensional representation of the iteration rule [math]a_{n+2} = \frac{a_{n+1}+k}{a_n}[/math]. Now, instead of always adding 1 to [math]a_{n+1}[/math], we can add something other than 1! The points plotted are of the form [math]\left(a_n,a_{n+1} \right)[/math].
Just observe the patterns before you decide to trace. Do there appear to be any other "nice" orbits (like our orbit of 5)? What happens when [i][math]k[/math][/i] is negative? What happens when [i][math]k[/math][/i] is zero? Do there appear to be any special values of [i][math]k[/math][/i]?
