Variants of the Duck-curve
Below you can see step 1 and step 2 of the Duck-curve again:
In step 1 of the Duck-curve, you can replace the blue line segment in the middle with the blue part from step 2.
You will then get the left image as step 1 and the animation on the right as a complete fractal:
What is striking is that the contours of this fractal increasingly resemble those of the Duck-curve. This is not illogical, because it is a variant of the Duck-curve.
This applies to all variants shown below.
The idea of replacing the middle line segment with step 1 of the Duck-curve can be carried further. Here are two examples:
Starting from step 2 of the Duck-curve (see above), the middle line segment can again be replaced by step 1 of the Duck-curve. You then get:
You can think of many more variations, but this gives a good idea of the possibilities.