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April 22, 2011
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Today I added some new stuff and organized my gallery in folders. The fractals I uploaded were made with formula combinations I'm testing lately, to see the possibilities of the fractal generator I'm writing. One of the good things is that I was able to implement and combine my "discovery", Mandelbrot on real numbers, with good results. After all is just an exponentiation of the real and imag values separately, then add to both values the modulus of the Julia constant modified by a multiplying factor (this is one of the variations I'm using). The original method for obtaining patterns was plotting the interference of two Mandelbrot formulas applied to real numbers, iterating them separately on x and y axis. I posted this on fractalforums.com, and gained the attention of that community, because of the curious patterns that emerged from that simple method without using complex values. This led later to the discovery of a "fractal waveform", a drawing that resembled a soundwave... Once I discovered why this drawing appeared, I wrote a VB code to make a sound file and sounded like wind gusts! It was funny to make that, but after all is only the waves produced by the mandelbrot iteration on the real axis, between the ranges -2, 0. If you plot this waves after each iteration, you get a bifurcation map... one of the simplest examples of how chaos emerges from the iteration of such a simple mathematical formula.
You can see the threads I mentioned here: [link] [link]
  • Mood: Joy
  • Listening to: Bjork
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:iconelement90:
I've tried the "real number Mandelbrot" and using a bailout of 4 I just get a square only when I reduce the bailout to 2 do I get the pictures shown in the fractal forums thread. I also tried cubing rather than squaring and I can't get anything other than a square.

I'll continue to experiment, if I get something I'm happy with I'll submit it as a deviation and let you know.
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:iconfractkali:
You won't get anything but this patterns, or variations of it. Julias are the same but less chaotic, and too strechted if the x and y values differs too much. The real deal is to do combinations, iterated with other formulas. I tried at first Tglad's "Ballfold" with good results, and the ones I'm posting lately are combined with "Ducks" formula, or regular Mandelbrots, all julia versions (I search the Mandelbrot version too see interesting zones, then do Julias with that coordinates). However, I use multiplying factors to fine-tune and match the combinations, because if not, the results are poor. Also I use inner coloring methods such as "exponential smoothing", no bailouts (I only use bailouts if combined with regular Mandelbrot, otherwise the values seems to fluctuate and don't diverge in the interesting zones. I can give you some more information if you want.
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:iconelement90:
I'd already discovered that different constant values for the x and y values in the Julia produce poor results. I mentioned that I wasn't getting the the same results as you with a bailout of, if I'd read further I would have discovered why. I've seen many references to the "Ducks" formula but I don't think I've found it yet or if I have I don't know any parameter combinations that produce good results. Do you know where I can find the "Ducks" formula?
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:iconelement90:
I've looked at the threads you've linked to on fractal forums. May I implement the "real number Mandelbrot" in my programs?
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:iconfractkali:
Yes, off course! I don't own anything, but if you can credit me in some of the artworks or software you publish using with this method, I'll appreciate that. Just as "Kali from fractalforums.com" Thanks!
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