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Dec 1, 2010 at 15:28 comment added Anixx Regarding the first example it is still interesting if the curve smooth when going through blue, red and part of the yellow zones (before the yellow curve crosses the $x=x_1$ point).
Dec 1, 2010 at 15:10 comment added Anixx It seems that the free term equal to 1 is a special case, it is indeed not smooth at $x_1$. If we take free term slightly greater than 1 we will get a self-circuited loop at any iteration, while if we take the term slightly smaller than 1 we will get a more smooth looking curve without loops.
Dec 1, 2010 at 15:01 history answered AppliedSide CC BY-SA 2.5