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Author Topic: One way to make a "real" 3-d mandelbrot set  (Read 1302 times)
Description: method for making foam free 3d "mandelbrot"
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Tater
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« on: September 29, 2014, 09:21:11 PM »

Begin with a mandelbrot in the plane, and rotate around the real axis, but instead of keeping the same parameters, vary one, say, the power of z, so that as we rotate through pi/2, we arrive at z_n+1=z_n^3+C, then drop the parameter back down again so that at pi/2, we are back to z_n+1=z_n^2+C. Of course, there are many different parameter variations one could use, especially if the iteration was written in polar variables rather than complex.

The continuous change should keep the infinitely complex bulb structure, and as the angle changes, there should be a continual smooth change in the location of the bulbs and tendrils.
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hgjf2
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« Reply #1 on: October 05, 2014, 10:16:42 AM »

Begin with a mandelbrot in the plane, and rotate around the real axis, but instead of keeping the same parameters, vary one, say, the power of z, so that as we rotate through pi/2, we arrive at z_n+1=z_n^3+C, then drop the parameter back down again so that at pi/2, we are back to z_n+1=z_n^2+C. Of course, there are many different parameter variations one could use, especially if the iteration was written in polar variables rather than complex.

The continuous change should keep the infinitely complex bulb structure, and as the angle changes, there should be a continual smooth change in the location of the bulbs and tendrils.
Yes, but this seem exacthly what I have written in my topic "A new idea for a "true" 3D Mandelbrot fractal set:Mandelbrot salad." on "New theory and research"
Can you post a graphic or scetck(draft on MSPAINT or manual on paper) how I have on this my topic?
Is interesting how to proceed as rotation at pi/2 and using cubic and squared Mandelbrot transformation.
 A peacock hrmm
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