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Welcome to Fractal Forums > Fractal Math, Chaos Theory & Research > Mandelbrot & Julia Set > The 3D Mandelbulb > Videos > At the frontier of the Mandelbulb
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Author Topic: At the frontier of the Mandelbulb  (Read 2809 times)
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gaston3d
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« Reply #15 on: January 05, 2010, 06:40:26 PM »
Quote from: bib on January 05, 2010, 01:20:12 PM
This is exactly what I meant : I want to find a nice minibulb and then move the camera backwards while increasing the magnification (maybe changing the image plane distance as well, I'll have to test), so that the minibulb keeps the same size while the background changes.

in this type of zoom i think camera FOV and distance sholud be in relation given:

\tan{\frac{\alpha}{2}} = \frac{\frac{1}{2}*x}{d}

where \alpha is camera FOV angle, x is object width, d is camera distance from the object, then

\alpha_{fov} = 2*\arctan{\frac{x}{2*d}}
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bib
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« Reply #16 on: January 05, 2010, 06:42:31 PM »
Quote from: kram1032 on January 05, 2010, 05:50:19 PM
Do you think, that would work? smiley

Yes that should work. A few weeks ago, I tried to do it in the 2nd order Mbulb, but results were not satisfying as you can imagine from the 2 pictures below, so I kept the cut-plane. I will try to do the same with higher powers.
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bib
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« Reply #17 on: January 05, 2010, 06:43:43 PM »
Quote from: gaston3d on January 05, 2010, 06:40:26 PM
Quote from: bib on January 05, 2010, 01:20:12 PM
This is exactly what I meant : I want to find a nice minibulb and then move the camera backwards while increasing the magnification (maybe changing the image plane distance as well, I'll have to test), so that the minibulb keeps the same size while the background changes.

in this type of zoom i think camera FOV and distance sholud be in relation given:

\tan{\frac{\alpha}{2}} = \frac{\frac{1}{2}*x}{d}

where \alpha is camera FOV angle, x is object width, d is camera distance from the object, then

\alpha_{fov} = 2*\arctan{\frac{x}{2*d}}


Thanks gaston for the maths.

Dave, can you make the script ? wink cheesy
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kram1032
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« Reply #18 on: January 05, 2010, 07:55:28 PM »
the 2nd order probably is too asymmetric for this kind of stuff... smiley
Already curiously waiting for higher order Msets smiley
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David Makin
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« Reply #19 on: January 05, 2010, 10:31:34 PM »
I just thought of a good analogy with respect to viewing the minibrots.

Take the complex z^8+c Mandelbrot and we can easily see the minibrots because we are 3D creatures and have a view of the entire plane.
Now imagine you are a 2D creature living somewhere on the plane "outside" the Mandelbrot and the Mandelbrot is rendered in the plane (say with colour for depth cueing) and you have the job of looking around to find and view the minibrots.
Essentially the task we face to find and view the 3D minibrots is the same.
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kram1032
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« Reply #20 on: January 05, 2010, 10:35:00 PM »
that's why 2D slices of different kinds could come in handy smiley

if the 2D-creatures could cut lines through the 2D M-set, they could under circumstances find out where such Minibrots are.

However, it would become totally mindblowing if they had to search through the 4D-set....... smiley
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bib
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« Reply #21 on: January 05, 2010, 11:00:46 PM »
I agree with you both and I found kram's analysis and explanations very relevant and convincing. And I realized just by looking again at the 2D z^8+c that the surface of the Mandelbulb is a totally crazy 3D maze as you approach the surface and follow the curves, the hills and valleys turning in all directions in 3D in a crazy dance!

So as suggested by kram, using a cut-plane, I focused on a "simple" and very symmetric minibulb: near the top of the main spike. But when I slightly move the cut plane, as you can imagine, it's just a mess, there are plenty of threads everywhere and it's not nice looking.

So I tried to use a spherical clip to show only the central part of the minibrot (not all the filaments), but I face 2 difficulties: 1 - finding the exact center coordinates of a minibulb is impossible to me, and 2 - I have frozen Dave's formula in UF just when I unchecked the cut-plane to see the final result. Sorry Dave, I did not save the upr and I can't replicate, I can't even remember how I did to do a mini-spherical clip on a minibulb.

So far, the best image I got is not much different from the blue image above, with a z^8+c instead of the z^2+c. I don't know what to do next. Maybe I should find how I did the mini-spherical clip, but anyway, I feel that it will not be what I'm looking for.
« Last Edit: January 05, 2010, 11:02:53 PM by bib » Logged
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kram1032
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« Reply #22 on: January 05, 2010, 11:49:36 PM »
maybe it helps to go inside the minibulb and look from there.
It might be easier to recognize certain details as the mess of dentrites around the minibulb wont show up that way...

Also try potential Minibulbs from different cut-planes smiley
Maybe for some strange reason a different Minibulb will have less mess around it...
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twinbee
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« Reply #23 on: January 06, 2010, 10:25:19 AM »
Quote
After some exploration of the Mandelbulb, I am a bit disapointed. Let me try to explain, and see if I'm right or wrong.

In the 2D M-Set, no matter where you zoom in at the border, you will always find a minibrot (if you know where to search it's easier). It means that no matter where you zoom in (e.g in the seahorse valley), you can still zoom in a minibrot's elephant valley for example, thus combining both regions' patterns in an intricate way.

I'm not sure if it's the same in the Mandelbulb. I *feel* that self-similarity is "stronger", meaning that once you have started to zoom in a particular area (they don't have "official" names like in 2D), for example the "crater" or "tower", or "bulb", or "cave", you have to stick with the patterns you find. For example if you start to zoom at the crest of a tower, you will hardly find minibulbs like if you had zoomed at first in a minibulb.

Don't know if I am clear enough. Any opinions?

Yes, it's true that the holy grail would be 1000x better still - that's why we're still searching. I see what you mean, the Mandelbulb is (almost, but not quite) like an organic version of the Menger Sponge, where patterns are pretty similar after zooming in.

But I still think we have a few surprises left, particularly on the inside of the bulb which has been hardly explored yet.
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