05/11/2009, 08:31 PM
(05/11/2009, 08:12 PM)sheldonison Wrote: Are the imaginary periods exactly repeating copies?
yes. \( F(z+T)=F(z) \).
Quote:The fractal behavior of \( F_{4,3} \) is \( F_{4,5} \) increasing to infinity via tetration, except it is occurring at the i=imaginary_period/2 line, with real values!
Yes! On the imaginary axis they are just translated by \( T/2 \). Isnt that strange!
Quote:It sounds as though the conversions are as simple as:
\( F_{2,1}(z)=F_{2,3}(z+\text{complexoffset1}) \)
\( F_{4,5}(z)=F_{4,3}(z+\text{complexoffset2}) \)
\( F_{2,3}(z)= F_{4,3}(z+\theta(z)) \),
Where the complex offset is just a real offset plus half of the imaginary period of each function.
Absolutely!
Quote:This means \( \theta \) along with the complex offsets, also allows conversions between \( F_{2,1} \) and \( F_{4,5} \), the lower superexponential, and the upper superexponential.
But \( \theta \) can not computed directly.