Gottfried Wrote:Here are some plots of that tri-furcation, see uncommented list below.

I find the bi-,tri- and multifurcation an interesting subject, as we ask: can we assign an individual value if the iteration oscillates/is furcated - since this is somehow related to the partial evaluation of non-convergent oscillating series, to which we assign a value anyway.

Yes, that is an interesting idea, that these seemingly convergent iterations are actually divergent but get the value in the same way like e.g. series 1-1+1-1..........= 1/2. What then, one would assign to the point which when iterated with on top oscillates between and ?

From complex geometric series , would we have to assign value to that Iteration by analogy with divergent (?) sum:

whose module is and argument , so value would be:

No, the sum is not the same as . First I have to generate such sum where only odd powers of I are present.

Ivars