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  So for this series, I was pondering the fact that we don't carry the signs of the magnitude for the imaginary component of the first part of the complex triplex:
complex_1 = x + sqrt ( y^2 + z^2) i  <---- no sign

  Now, this really doesn't effect the calculations of the 2d set, as can be seen visually (2d Mandelbrot is reflected over the x axis) or mathematically (I wrote a maxima formula to check the variations).  However, for the 3d set we end up with a variation when the y pixel component changes sign (for all even z^n: n= 2,4,6,8..... a positive y pixel component yields a different magnitude result from a negative y pixel component).

  So this got me thinking (again) about ways to correct the issue (absolute value anyone?), but I'd already done the absolute value of the pixel components and made a "corrected" 3d Mandelbrot (that was adequately detailed for z^2), so I decided to experiment with taking the absolute value of specific components (a lot like the Burning Ship fractal (http://en.wikipedia.org/wiki/Burning_Ship_fractal)).

  I ended up making several interesting discoveries, including the fact that the regular 3d complex triplex gains TONS of details when you correctly apply +/- and absolute values to the various components.  Many absolute value/sign combinations are discontinuous, only certain ones work (the hints in my new formula set (under complex compound corrected version) tell you the main combos of values/signs that I found to be continuous).  

  Anyways, here are a few of the images I made recently.... I didn't even include the 7th order zoom series, which shows some really cool details...

4th order:
(http://lh3.ggpht.com/_gbC_B2NkUEo/TJ1J-94-ZiI/AAAAAAAAAsQ/HzdH1K3j4d8/zoom%20on%20the%20spine.jpg)
5th order:
(http://lh6.ggpht.com/_gbC_B2NkUEo/TJ1J_GFY5-I/AAAAAAAAAsU/0NuR4kbsVJo/big%20one%20nice%20mode.jpg)
5th order:
(http://lh5.ggpht.com/_gbC_B2NkUEo/TJ1J_aNyuTI/AAAAAAAAAsY/_LZRphlYKK8/somewhere%20in%20bigone%20nice%20mode.jpg)
6th order:
(http://lh6.ggpht.com/_gbC_B2NkUEo/TJ1J_jlOXRI/AAAAAAAAAsc/ljDMpQHA3Yw/razzle%20dazzle%20top.jpg)
6th order
(http://lh4.ggpht.com/_gbC_B2NkUEo/TJ1K9k4ACcI/AAAAAAAAAso/D6aFZaswqN0/6th%20order%20experiment.jpg)
8th order (full size here) (http://lh3.ggpht.com/_gbC_B2NkUEo/TJ1K975Gx2I/AAAAAAAAAss/vM5ATspmIF4/tower%20big.jpg)
(http://lh3.ggpht.com/_gbC_B2NkUEo/TJ1K975Gx2I/AAAAAAAAAss/vM5ATspmIF4/tower%20big.jpg)
8th order, bluffs near the tower (http://lh5.ggpht.com/_gbC_B2NkUEo/TJ1K-Ig7D3I/AAAAAAAAAsw/RPBP0nyE8Ok/the%20bluffs%20near%20the%20tower.jpg):
(http://lh5.ggpht.com/_gbC_B2NkUEo/TJ1K-Ig7D3I/AAAAAAAAAsw/RPBP0nyE8Ok/the%20bluffs%20near%20the%20tower.jpg)
8th order spinners (full size here) (http://lh6.ggpht.com/_gbC_B2NkUEo/TJ1K-sDKchI/AAAAAAAAAs0/VZGsymui9MY/nice%20one.jpg):
(http://lh6.ggpht.com/_gbC_B2NkUEo/TJ1K-sDKchI/AAAAAAAAAs0/VZGsymui9MY/nice%20one.jpg)

2nd order straight on large (view full size here): (http://lh5.ggpht.com/_gbC_B2NkUEo/TJ1J-mPF5UI/AAAAAAAAAsM/LnH6AmtyJk0/big%20straight%20on.jpg)
(http://lh5.ggpht.com/_gbC_B2NkUEo/TJ1J-mPF5UI/AAAAAAAAAsM/LnH6AmtyJk0/big%20straight%20on.jpg)