Title: complex compound method Post by: M Benesi 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: (http://lh5.ggpht.com/_gbC_B2NkUEo/TDQzPmV-tTI/AAAAAAAAAiQ/cg8CrNx670s/warm%20ice.jpg)(http://lh4.ggpht.com/_gbC_B2NkUEo/TDQzPwAggPI/AAAAAAAAAiU/NTxBgvglN3g/nice%20ice.jpg) z^2: (http://lh3.ggpht.com/_gbC_B2NkUEo/TDQ1srVcLsI/AAAAAAAAAio/lVqWAmXSVqQ/Quick%20hit%20zoom.jpg)(http://lh4.ggpht.com/_gbC_B2NkUEo/TDQ092l0zAI/AAAAAAAAAic/VhZEVZae4F8/Quick%20hit.jpg) z^5: (http://lh6.ggpht.com/_gbC_B2NkUEo/TDQzPRoo27I/AAAAAAAAAiM/WVjK6la1_mw/quicky.jpg) Title: Re: complex compound method Post by: Rathinagiri on July 07, 2010, 10:52:55 AM Looks so great!
Flowers on the 3rd and 4th are really wonderful. Title: Re: complex compound method Post by: M Benesi on July 08, 2010, 09:50:54 PM Thanks. :D
If anything, it's interesting to see that combining 2 mandelbulb variations (complex triplex versions) results in interesting original fractals. Title: Re: complex compound method Post by: jehovajah on July 16, 2010, 08:46:15 AM Very organic!
Can I ask why you call it a compound formulation? Title: Re: complex compound method Post by: M Benesi 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). |