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. [br][br]The points plotted are of the form [math]\left(a_n,a_{n+1} \right)[/math]. The coordinates of point A are [math]\left(a_1,a_2 \right)[/math], so moving point A changes the value of the first two terms of the sequence. Click on point A and use the arrow keys on your keyboard to move point A.

Just observe the patterns before you decide to trace. [br][br][list][*]Do there appear to be any other "nice" orbits (like our orbit of 5)? [br][/*][*]What happens when [i][math]k[/math][/i] is negative? [br][/*][*]What happens when [i][math]k[/math][/i] is zero? [br][/*][*]Do there appear to be any special values of [i][math]k[/math][/i]?[br][/*][/list]