08/13/2010, 06:47 AM

From examining the superfunction for 4z(1-z) about z=0, (one of the few elementary examples for a non-Mobius function), we get:

So [one of] the iterate of is . Putting these functions into the "Mandlebrot" form by conjugating with , we get that the iterate of is .

I was hoping to include some pictures of the Julia sets of these two functions, but I don't have ready access to a program that can draw general cubic sets (such as the old Autodesk Chaos program). So I'll try again in the morning, using Fractint.

So [one of] the iterate of is . Putting these functions into the "Mandlebrot" form by conjugating with , we get that the iterate of is .

I was hoping to include some pictures of the Julia sets of these two functions, but I don't have ready access to a program that can draw general cubic sets (such as the old Autodesk Chaos program). So I'll try again in the morning, using Fractint.