negative mandelbulb - has anyone expored a bulb from inside out?

[Mrz00m]

Is it possible to make the void area surrounding the mandelbulb a solid, and to to make the actual mandelbulb a void, and then to place the camera within the bulb and explore from inside out?

I think the nature of the surfaces would be completely different as viewed from inside, because it would be more spikey and have millions of concave recesses, rather more like the 2d mandelbulb looks like.

are there already inverse bulbs?

[Syntopia]

Yes, some of the images on Daniel White's site are inside renders, search for 'inside' on this page: http://www.skytopia.com/project/fractal/mandelbulb.html

And yes, they do look great!

[cKleinhuis]

has any 3d renderer implemented pre-transforms ? e.g. z=1/z before iteration ?!?!?

[Mrz00m]

oooh i found the inside one when i knew what to look for. (incidentally did you see the google chrome experiments interactive   http://www.chromeexperiments.com/detail/the-rational-keyboard/ )

here is the closest i have seen to the 3d textures of an inverse bulb, image by jos leys from miquel''s page:
http://www.miqel.com/images_1/fractal_math_patterns/3-dimensional-fractal/mandelbulbs_sliced.jpg

cKleinhuis i dont understand the maths, i will have a go at this z=1/z.  How it possible to do a spherical 3d bulb based on the first image in yellow and also from these ones? http://paulbourke.net/fractals/mandelbrot/inverse.gif

[KRAFTWERK]

Hello Mrz00m

This idea is as old as the mandelbulb itself...
Today you can explore the inside of most fractals with mandelbulb 3D.
Here are some images I did with MB3D:
http://www.fractalforums.com/index.php?action=gallery;sa=view;id=6008
http://www.fractalforums.com/index.php?action=gallery;sa=view;id=5931

You should also check out Trafassels and Buddhis images and videos here on fractalforums, they have done many beautiful inside shots.

[Mrz00m]

oh that's excellent, sorry i thought there must be some internal views of bulbs around but i didnt know what i was looking at when i saw them because i thought they would look completely different, i thought it would be as equally spikey as the mandelbulb is blobby. it confirms that the bulb has elements of a quaternion transformation stretching joining together some very recursive areas. It would be nice to see some 3d versions of the spirals from the 2d mandelbrot, i think that bib did some vids of various spirals, but i am still waiting to see some parameters for some spirals?!

what about an actual self contained 3d version of of 1/z and 1/c to power of 8?

the inside and out prove that the specific shapes of the 2d set cant's be observed as from a theoretical "inside" or "ourside" of the bug because the 2d mset shape is only the form of the border that cant be seen from within or wihout.

here are some shapes from sphereinvY/intpow/yplussinz

[DarkBeam]

Jesse did it a long ago!

http://www.fractalforums.com/index.php?action=gallery;sa=view;id=5864

 

[DarkBeam]

here are some shapes from sphereinvY/intpow/yplussinz

sphereinvY is not a sphere inversion, more a curious 3D transform I found by accident

[Mrz00m]

oh, it's seems to produce almost the same effect as a 1/x reciprocal y formula if placed before the bulb iteration, except that reciprocal X and Y extend to infinity so the features further from the origin are all smudged whereas the sphereinvY does a reciprocal y function but rounds it beyond y>1 into a bubble, it is great! i thought that it might make a radial symmetry of a sphere over itself so that all the sphere coords near the boundry are reflected to the centre and the points at the centre become the new sphere boundry. is there a symmetry of a sphere so that the axis of symmetry is the actual boundary of the sphere?

[Alef]

has any 3d renderer implemented pre-transforms ? e.g. z=1/z before iteration ?!?!?

I would suggest using c=recip(pixel); as pre transform. I did that on Chaos pro. It looks better than c=1/pixel. Aof corse in quaternionic numbers.