01/18/2008, 05:50 AM
Ivars, I think I know what you might be talking about, or at least, I have something that may be described in similar words. This is a 3D plot of the function \( b^{b^x} - x \) and a 3D plot of "zero". The interesting thing here, is that the intersection of the two is what we are trying to parameterize. You can see the intersection of the two in this plot:
What is also interesting about this plot is that is shows (in some sense), why the outer "legs" should be attracting periodic points, and the middle is a repeling fixed point. It shows this because the slope/derivative is in the opposite direction fot the middle than it is for the other two branches/legs.
Andrew Robbins
What is also interesting about this plot is that is shows (in some sense), why the outer "legs" should be attracting periodic points, and the middle is a repeling fixed point. It shows this because the slope/derivative is in the opposite direction fot the middle than it is for the other two branches/legs.
Andrew Robbins