(08/30/2010, 11:08 AM)tommy1729 Wrote: ok that makes some sense.Using base b= sqrt(2)

now explain me what you are doing in this thread and WHY ?

- what is the height-representation of 3 ?

By Kousnetzov? By Robbins slog? By regular-tetration using fixpoint 2? using fixpoint 4?

Quote:and WHY is f(z) periodic ???

Code:

`ยด`

f(z) = ... z^^-3 + z^^-2 - z^^-1 + z - z^^1 + z^^2 - z^^3 +...

let y=b^b^z = z^^2

f(y) = ... y^^-3 + y^^-2 - y^^-1 + y - y^^1 + y^^2 - y^^3 +...

= ... z^^-1 + z - z^^ 1 + z^^2 - z^^3 + ...

= f(z)

f(z) and f(y)=f(z^^2) are equal => f(z) is periodic in terms of the height-parameter

Quote:how to compute its period ??

f(z) = f(z^^2) where z^^2 = b^b^z ==> period-length is delta_h = 2

It is more difficult to find the amplitude

Gottfried Helms, Kassel