3D Mandelbub and non trivial cylindrical symmetry.

[MTd2]

Hi people! I am new here! 

So, according to this article "The Unraveling of 3D Mandelbub", page 2, http://www.skytopia.com/project/fractal/2mandelbulb.html , one can see that both power 2 and power 3 have trivial symmetry, that is one can rotate the set 180º along the main axis and one get the same picture. Power 8 one can count a 7 fold symmetry, and increasing as the power goes up.

This is a really strange pattern, given that the non trivial cylindrical symmetry spontaneously emerge somewhere after power 3, but it is not clear to me when. I guess this is an aspect of what people call interesting but wasn't clarified.

Could anyone show the intermediate powers from 4 to 7?

[bib]

Hi

You can see power 6 here:
<a href="http://www.youtube.com/v/LxsniUIVfEM&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/LxsniUIVfEM&rel=1&fs=1&hd=1</a>

And I am preparing a video that shows the morphing from power 1.5 to 8

[MTd2]

That one has 5 fold symmetry. So the non trivial symmetry should appear at power 4. So why 8 is more interesting than 4,5,6,7?

[bib]

That one has 5 fold symmetry. So the non trivial symmetry should appear at power 4. So why 8 is more interesting than 4,5,6,7?

watch the video here (reply #24)
http://www.fractalforums.com/3d-fractal-generation/3d-mandelbrot-using-ultrafractal-5/15/