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 Tetration of complex bases to complex towers andydude Long Time Fellow Posts: 509 Threads: 44 Joined: Aug 2007 11/04/2009, 03:01 AM (This post was last modified: 11/04/2009, 03:02 AM by andydude.) (11/03/2009, 08:52 AM)mike3 Wrote: ... the kidneybean ... lol, I call it the Shell-Thron region, or "the shell" for short, which oddly enough describes both the author and the shape. So how about the base $b = 3 + i$. The intuitive/natural Abel function of exponentials associated with this base is: $\text{slog}_b(x) = -1 + (0.984001 + 0.124042 i)z + (0.246854 - 0.0364779 i)z^2 + \cdots$ when expanded at 0. It seems to be fairly close to being real-valued for arguments around 0 to 1. I have attached 2 plots, the critical function above, and the piecewise extension to all R. Blue is the real part and red is imaginary part. Andrew Robbins Attached Files Image(s) « Next Oldest | Next Newest »

 Messages In This Thread Tetration of complex bases to complex towers - by mike3 - 10/26/2009, 03:29 AM RE: Tetration of complex bases to complex towers - by andydude - 10/29/2009, 05:48 AM RE: Tetration of complex bases to complex towers - by mike3 - 11/01/2009, 12:37 AM RE: Tetration of complex bases to complex towers - by andydude - 11/03/2009, 08:00 AM RE: Tetration of complex bases to complex towers - by mike3 - 11/03/2009, 08:52 AM RE: Tetration of complex bases to complex towers - by andydude - 11/04/2009, 03:01 AM RE: Tetration of complex bases to complex towers - by mike3 - 11/04/2009, 05:29 AM RE: Tetration of complex bases to complex towers - by andydude - 11/06/2009, 05:13 AM RE: Tetration of complex bases to complex towers - by mike3 - 11/06/2009, 08:46 AM

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