Cyclic Driven IFS

3-Cycles

The repeating pattern

T₁ followed by T₂ followed by T₃

produces a sequence converging to the three points with addresses

(321)^infinity, (132)^infinity, and (213)^infinity.

Click the left picture for an animation illustrating this. The right picture shows the three points to which these sequences converge, along with their addresses.

Click to animate.

Here we use addresses of the 3-cycle points to find the combination of transformations for which each is a fixed point.

Here we use the fixed point equation to find the coordinates of the 3-cycle points

Here we investigate what happens if we apply the transformations in a different order.

Return to Cyclic IFS.