The Steps of the Sequence and Invariant Curve
- Steve Phelps
This representations of the repeated iteration of should be downloaded. The points are colored based upon where they are located when k=1. You can also reveal the orbit of the points by using the step slider. Move point A to change the values of the first two numbers in the sequence. Drag the slider k to change what is being added in the numerator. The invariant curve has the equation where C in a constant. There are up to 200 points displayed. When you download the files, show the Spreadsheet View and add more points by filling more points down.
- Does there appear to be other orbits with periods different from 5?
- What kinds of symmetry do you notice?
- Does there appear to be any "special" values of k?
- Does there appear to be any special locations for point A?