complex compound method

[M Benesi]

  Yet another fractal variation.  This is the latest complex compound that I've been working on, a very basic compound equation that combines 2 complex triplex formulas into one (so as to have a more "balanced" approach).  It's a combo of the x vs. yz mag and the xy mag vs. z complex triplex formulas (which are faster versions of the trig bulbs, at least on my old computer without a modern GPU). 

  Anyways, a few images:

z^3:

z^2:

z^5:

[Rathinagiri]

Looks so great!

Flowers on the 3rd and 4th are really wonderful.

[M Benesi]

   Thanks. 

  If anything, it's interesting to see that combining 2 mandelbulb variations (complex triplex versions) results in interesting original fractals.

[jehovajah]

Very organic!

Can I ask why you call it a compound formulation?

[M Benesi]

  It's a combination of several complex triplex formulas.

  Basically, I do an iteration of:
x vs. magnitude y and z, and y vs. z
  then an iteration of:
y vs. magnitude z and x, and z vs. x
  then an iteration of:
z vs. magnitude of x and y, and x vs. y

  By complex triplex, I mean using complex numbers to calculate triplex numbers.

triplex (x,y,z)^n =

x= the real part of the complex number (x +  i sqrt (y^2+z^2) )^n
y= the imaginary part of the complex number (x + i sqrt (y^2+z^2))^n * the real part of the complex number (y + i z)^n * the magnitude of y and z to the -n, sqrt(y^2+z^2) ^-n
z= the imaginary part of the complex number (x + i sqrt (y^2+z^2))^n * the imaginary part of the complex number (y + i z)^n * the magnitude of y and z to the -n, sqrt(y^2+z^2) ^-n

  For the y and z components, you need to divide out the magnitude of y and z when it is applied 2 times (once in the x vs y and z part, and once in the y vs. z part).