I think you call this formula the 'flipped' one :
z= (R^(@pow/2))*sin(@pow*ph)*exp(i*@pow*th)+c1
zz=(R^(@pow/2))*cos(@pow*ph)+cz
R=(|z|+zz*zz)
th=atan2(z)
ph=atan2(zz+i*cabs(z))
if ph>=#pi/2,ph=#pi-ph,endif
Thanks Jos. Yes, that is the 'flipped' version.
To recap, the reason for the parity changes in some versions is to get equivalence between forward and inverse iteration for a given formula, which is necessary due to phi giving a double cover when iterated beyond 0 to pi.
The usual forward iterations have no parity change (of course), and to reproduce them using MIIM we have to add some parity change in the inverse method.
This flipped version originally resulted from a cosine phi inverse iteration without any parity, which turned out to be often more interesting than the one with correct roots. To duplicate it in forward iteration requires a parity change there instead.
However, that simple parity formula is only "correct" for integer powers, so you've discovered another useful mutation. If you haven't already tried it without the parity change to phi, that would give the "true" cosine version, which should be asymmetric. I haven't figured out how to reproduce this flipped Glynn inversely.
May 19, 2010, 03:11:42 PM
Dilber MC Theme by HarzeM