What-If-Not: The Original Problem in 2D
- Steve Phelps
This is a 2-dimensional representation of the iteration rule . Now, instead of always adding 1 to , we can add something other than 1. The points plotted are of the form . The coordinates of point A are , 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.
- Do there appear to be any other "nice" orbits (like our orbit of 5)?
- What happens when is negative?
- What happens when is zero?
- Do there appear to be any special values of ?