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Author Topic: Inner view of the Mandelbox  (Read 29987 times)
Description: The Mandelbox (by Tglad) - Inner View
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trafassel
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trafassel
« Reply #135 on: October 25, 2010, 01:46:18 AM »

Attractor with scale=-1.03


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trafassel
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trafassel
« Reply #136 on: October 25, 2010, 02:40:20 AM »

Outer view, but changing scale factor (from -1.3 to -1)


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trafassel
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trafassel
« Reply #137 on: October 25, 2010, 02:50:21 AM »

The surface structure reminds me of thic picture of a disco ball in the -1.1minRad0Mandelbox.


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trafassel
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trafassel
« Reply #138 on: October 26, 2010, 09:48:26 PM »

This is also an ouside picture: a tunnel. Scale =-1.03



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trafassel
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trafassel
« Reply #139 on: October 26, 2010, 10:07:27 PM »

A typical "Inside" tunnel.


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trafassel
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trafassel
« Reply #140 on: October 26, 2010, 10:10:37 PM »

A symmetric multi tunnel.


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gussetCrimp
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« Reply #141 on: October 26, 2010, 10:30:48 PM »

These are so interesting - any chance of a fly-through of the insidebox?

(Just to be sure: the space you would be flying through, and that the "camera" is in for all these images, is where the "normal" Mandelbox has solid walls--and not just some space that is inside the normal Mandelbox, right? I keep getting confused! In other words it's the complement of the Mandelbox?)

Can you just flip a sign in the formula, and use the software to make an animation in exactly the same way as for the "normal" Mandelbox? Or is it more complicated than that?
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Tglad
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« Reply #142 on: October 27, 2010, 02:31:27 AM »

There's a nice video a couple of pages back.
Yes, its the compliment of the mandelbox, but I don't think you can just flip a sign, it is harder to draw the inside of a fractal because there's no threshold so you have to iterate to the maximum number of iterations for each point along the ray for each pixel. (I think). So I think it is slower to calculate.

An interesting thing about the inside of the mandelbox is we think it is nowhere dense... so the inside views actually have structure everywhere... if you take any empty bit of space and look in really high detail I think there will be little strings of bubbles or fractal trees filling the space.
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trafassel
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trafassel
« Reply #143 on: October 27, 2010, 09:44:05 PM »

Yes, an inside video needs a lot more rendering time than an outside video. Tglad gives a good explanation, why the additional time is needed.

The "nowhere dense" hypothesis is new to me. I think, I can define an area in the -1.1minScale0Mandelbox where each point in this set is element of the Mandelbox set. But let me think about this.

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trafassel
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trafassel
« Reply #144 on: October 27, 2010, 10:41:18 PM »

In a 4-dimensional Mandelbox the objects appears more sparse.


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trafassel
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trafassel
« Reply #145 on: October 27, 2010, 10:57:30 PM »

In a 4-dimensional Mandelbox you can combine different fractal shapes into one objects.


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visual.bermarte
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« Reply #146 on: October 27, 2010, 11:26:39 PM »

the last one is a total upgrade of Fridolin!
smiley
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trafassel
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trafassel
« Reply #147 on: October 27, 2010, 11:57:18 PM »

Sparse 4-dimensional Mandelbox scene.


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Tglad
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« Reply #148 on: October 28, 2010, 12:13:28 AM »

I'm sorry? 4 dimensional mandelbox? .. woah afro a 3d slice of it, I've never seen it before.

The nowhere dense idea is because there are no attractors (unlike 0+0i on mandelbrot) and so it is more like a menger sponge that happens to be a thicker sponge towards the middle. There is no area of the mandelbox that doesn't have tiny holes or cracks in it.
So reversing the logic, there is no area of space in the compliment mandelbox that doesn't have structure in it. A completely untested idea smiley

The funny shapes of concentric circles are actually 'detractors', points straying too close to the centre of them get thrown towards infinity.
« Last Edit: October 28, 2010, 12:22:33 AM by Tglad » Logged
trafassel
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trafassel
« Reply #149 on: October 28, 2010, 11:53:40 PM »

In the 4-D Mandelbox I added another folding operation (symmetric to the other x,y,z-foldings).

The original idea was given in:
http://www.fractalforums.com/3d-fractal-generation/folding-boxes-in-higher-dimentions/
but in interpreded the "higher dimension folding" not in this strong sense.

(Formula in: http://github.com/trafassel/Gestaltlupe/blob/master/settings/Public/Unsorted/Data493pic10164.tomo)

Now the "nowhere dense idea" makes sense for me. Has anyone try to prove this?

Another open question: How many monsters?

<a href="http://www.youtube.com/v/-3mZflTJEqU&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/-3mZflTJEqU&rel=1&fs=1&hd=1</a>
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