Cyclic Driven IFS

Here we will learn to recognize the visual signature of IFS driven by cyclic data, that is, numbers that repeat a particular pattern.
The simplest repeated sequence is constant, just repeat the same number.
Constant sequences generate sequences of points that converge to the fixed point of the corresponding transformation.
The next simplest repeated sequence is a 2-cycle, it alternates between two values.
Here we find the addresses of the 2-cycle points.
Here we find the coordinates of the 2-cycle points.
How do the limiting points depend on the choice of initial point?
Repeating a pattern of three transformations produces a 3-cycle.
Here we find the addresses of the 3-cycle points.
Here we find the coordinates of the 3-cycle points.
What happens if we apply the 3-cycle transformations in a different order?
General cycles

Return to Driven IFS.