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Author Topic: complex compound method  (Read 845 times)
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M Benesi
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« on: July 07, 2010, 10:07:52 AM »

  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:



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Rathinagiri
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« Reply #1 on: July 07, 2010, 10:52:55 AM »

Looks so great!

Flowers on the 3rd and 4th are really wonderful.
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M Benesi
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« Reply #2 on: July 08, 2010, 09:50:54 PM »

   Thanks.  cheesy

  If anything, it's interesting to see that combining 2 mandelbulb variations (complex triplex versions) results in interesting original fractals.
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jehovajah
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« Reply #3 on: July 16, 2010, 08:46:15 AM »

Very organic!

Can I ask why you call it a compound formulation?
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M Benesi
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« Reply #4 on: July 16, 2010, 08:36:57 PM »

  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).
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