Cyclic Driven IFS

Choice of Initial Point

How do the limiting points depend on the choice of (0.5, 0.5) as starting point? Not at all.

This should be no surprise: recall the attractor of an IFS does not depend on the initial picture. (This is a bit different than the situation at hand, however, but certainly makes the result plausible.)

Here is an illustration. We follow the sequences generated from three different starting points, all with vertices selected in the order 121212... = (12)^infinity. Blue lines for one starting point, green for the second, red for the third.

Click the picture to start the animation.

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