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 Author Topic: Higher Iterations  (Read 13745 times) Description: How the interior of a minibulb is filled on higher iterations. 0 Members and 1 Guest are viewing this topic.
trafassel
Fractal Bachius

Posts: 531

 « Reply #15 on: January 18, 2010, 06:49:59 PM »

On the top of the tower, the whipped cream seems to converge.

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Timeroot
Fractal Fertilizer

Posts: 362

The pwnge.

 « Reply #16 on: January 18, 2010, 06:57:26 PM »

This reminds me somewhat of how, at the "entrance" to a Julia set (in th regular 2D MSet), the iterations can start to remove very little each time, but eventually they "squeeze" through the "entrance" and sort of "blossom" out again into smoother curves. But they converge anyway. The way that this iterations of the MSet seem to stop at sharp edges and then inflate again into whipped cream seems like a very similar mechanism... would this imply that the 3D tier being built would be some kind of corresponding part to a Julia Set?
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Someday, man will understand primary theory; how every aspect of our universe has come about. Then we will describe all of physics, build a complete understanding of genetic engineering, catalog all planets, and find intelligent life. And then we'll just puzzle over fractals for eternity.
kram1032
Fractal Senior

Posts: 1863

 « Reply #17 on: January 18, 2010, 07:16:07 PM »

Thinking about it and looking at the iteration-sequences:

It looks like (if you look at the inside) whipped cream is simply an area of growth, happening after the fractal details in the previous level of whipped cream got too tiny.
Maybe, this happens after fractal detail reaches a special generally calculable, uhm..., fractalillity, which could possibly help to find "perfect" iteration levels, where most details in the current layers are present.

Maybe, "tools" could be found to "cut" parts out of the set like single nerves from bodies.

In case of the 2D-set, if you imagine a person to have a surgery, who comes from the flatlands, it would be a piece of cake to do so: You wouldn't even have to cut him open as you already see what's on the inside and could directly alter the inside that way.
Surgeries would be as simple as ever possible.

But try to find a single blood vessel in a 3D-human being. - Tools to cut open without harming too much are needed. So, let's develop nice "knife"-tools to lay free structures of the boundary, hidden under other levels of detail...

Actually, what's whipped cream in the Mbulb could be comparable with connective tissue in our bodies - those thin skin-like structures just hold other parts of us together. In between, we have hour organs of different fractality
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Timeroot
Fractal Fertilizer

Posts: 362

The pwnge.

 « Reply #18 on: January 18, 2010, 08:03:38 PM »

This is going a little off-topic, but what if we could see in 4D?

Improvements for artificial eyes are improving rapidly, and I don't know quite how good they are, but I think I read that they've shown the brain can adapt to correctly interpret the signals being sent by a camera.

Couldn't it theoretically be possible to transmit 4D visual information to the brain?

Couldn't the brain adapt, allowing us to see all four dimensions correctly?

Wouldn't this crazy pwnge?

It would take a very long time, I guess, for the brain to figure it out, but once it did... that's be awesome. Imagine being able to see the entire Julibrot set's surface - no slicing. Imagine being able to see a full quaternion Julia's surface. We could also use that to see the entire Mandelbulb laid flat. So I say: wait 40 years for insanely awesome android eyeballs, then it should be easier.
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Someday, man will understand primary theory; how every aspect of our universe has come about. Then we will describe all of physics, build a complete understanding of genetic engineering, catalog all planets, and find intelligent life. And then we'll just puzzle over fractals for eternity.
kram1032
Fractal Senior

Posts: 1863

 « Reply #19 on: January 18, 2010, 08:18:59 PM »

I'd rather directly go for 5D as many of those sets need 5 Dimensions to be laid flat.
You know: It's one way to get the brain to refactor 3D-views as for that it already has a certain fixed (more or less flat) area, but even if you could send 4D-images to the brain, finding a way to adapt the optical field to allow such a projection, how would you get it to learn 4D-movements? As long as it doesn't, all the interpretations will look 3D, as the 4th Dimension doesn't change.

I don't say it's impossible, but you really'd have to play with more than just the visual system. Also the movement-system needs to be affected...

"Easiest" would be to use "3D" glasses which however project 4D-stuff to your eyes and one of those headbands, measuring brainwaves (EEG however not too accurate, afaik) together with muscular "waves" (MEG) and uses that data to control a computer.....

Basically, to "move", through that 4D-environment, you need to "think to move". The computer interprets the data from the brain, the brain interprets the visual data obtained and by that, you could learn

However, I really don't know how you would do those 4D-pictures... Just by rotating around it like with a 3D-object, you don't get a full 4D-vision.

You'd very likely need a mix of 3D and 4D images, learn "both" (or are there more) kinds of rotation in 4D and apply those to 3D....

\OT end
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Timeroot
Fractal Fertilizer

Posts: 362

The pwnge.

 « Reply #20 on: January 18, 2010, 09:20:48 PM »

Yeah, you could use a EEG/MEG to move around, or just a simple keyboard. It's true that by moving around you wouldn't see the entire 4D object - but the same is true for 3D. We can't see the entire Mandelbulb, even with rotation. I think that if we can transmit two sets of 2D information to build up a 3D perspective, we should be able to deliver two sets of 3D information to build up a 4D perspective, don't you think? It would require a pretty fast bus speed for the brain, and a fast computer to be responsive, but it would open up so much if it worked.... can you imagine a 4D MMORPG? Graphic design would be something totally new.
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Someday, man will understand primary theory; how every aspect of our universe has come about. Then we will describe all of physics, build a complete understanding of genetic engineering, catalog all planets, and find intelligent life. And then we'll just puzzle over fractals for eternity.
kram1032
Fractal Senior

Posts: 1863

 « Reply #21 on: January 18, 2010, 11:34:44 PM »

4D perspective isn't actually hard:

Just the same equations:

first two Dimensions are undistorted and the other two have perspective distortion

I once tried to draw 4D perspective hypercubes by hand

Worked not too bad. All you need is two points of infinity rather than 1.

You could also add perspective to the first two dimensions which in some pieces of art is a trick to let you uncertain about where's up and where's down and such.

AFAIK, an example are those pieces of art of infinite staircases with monsters going everywhere. You can't be sure if you're looking down or straight forward or even up due to perspective irritations

\second attempt on OT end
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twinbee
Fractal Fertilizer

Posts: 383

 « Reply #22 on: January 19, 2010, 12:31:19 AM »

Great anim trafassel!

Quote
Maybe, a glow-ish buddhabrot variant (or in general a transparent one) could help with the look.

Translucency sounds ace, but will have to wait until I incorporate a scan of more than just the visible shell into my renderer. Maybe one could use a glow based on the surface normal (in relation to the camera, perhaps so that viewing the surface head on will appear least brightest).

I'd like to animate this smoothly, but it would be nice to be able to render a continuous realm of iterations (instead of the discrete/integer amount that the Mandelbulb uses intrinsically).

Cross sections of the above pics would be intriguing too. Sigh, so much to do, renderer and mandelbulb wise!

Quote
Couldn't it theoretically be possible to transmit 4D visual information to the brain?
Couldn't the brain adapt, allowing us to see all four dimensions correctly?

I doubt we can truly 'grok' 4D very well. We can't really even see 3D properly (otherwise we'd be able to see through and all stuff simultaneously) - it's more 2 times 2D (i.e. 2 eyes x 2D pixel arrays).

Quote
Worked not too bad. All you need is two points of infinity rather than 1.

Heh, yeah that's cool - is that how 4D is often visualized? 3D is already cramming loads of hacks onto 2D (light/dark shading, perspective distortion, two eyes, blurring etc.), so maybe one or more of those hacks could be 'borrowed' for 4D in a more intuitive way.

Quote
\second attempt on OT end

Failed
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kram1032
Fractal Senior

Posts: 1863

 « Reply #23 on: January 19, 2010, 01:21:31 AM »

xD

Well... I guess, as there is no way to have 3 eyes, which, with a shift also in the 4th axis for the 3rd eye in theory would allow 3x2D -> 4D vision, you actually'll HAVE to borrow the 2 eyes

Perspective would be extended to just an other point.

light rules like reflection/refraction and stuff would work the same as they already are restricted to the plane between the ray and the surface-normal of the reflecting/refracting object at the point, the ray hits the object (long explanation for a very short meaning xD).
From the optical point of view, 4D probably isn't that much more complex than 3D. The equations stay more or less the same but things (assuming a monte carlo-style raytracer) will need way longer to clear up.

interesting would be some strange reflection and refraction (prism and lens) setups to direct to-us-invisible 4D-rays directly into the 3D world.
would just be a matter of directing rays to a 0-valued 4th dimension. The simple, trivial hyper"plane" (our space) which has the equation (w,x,y,z as coordinates) z=0

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KRAFTWERK
Global Moderator
Fractal Senior

Posts: 1439

Virtual Surreality

 « Reply #24 on: January 19, 2010, 10:17:06 AM »

Beautiful and very interesting renderings.

Curious to see how higher iterations gradually “builds up new layers” in your renderings Twinbee.
Makes me want to make thin slices of the last render, with the higest iterations.
And theoretical research would be very nice to follow here trafassel!

Keep on iterating!

(Love the OT in this thread as well )
 « Last Edit: January 19, 2010, 10:21:49 AM by KRAFTWERK » Logged

trafassel
Fractal Bachius

Posts: 531

 « Reply #25 on: January 19, 2010, 11:48:03 AM »

I'd like to animate this smoothly, but it would be nice to be able to render a continuous realm of iterations (instead of the discrete/integer amount that the Mandelbulb uses intrinsically).

In the first part of my animation i simulate the  continuous realm of iterations by decreasing the escape distance in the iteration itself.
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trafassel
Fractal Bachius

Posts: 531

 « Reply #26 on: January 21, 2010, 02:06:26 AM »

... on the border of the spine.
 Data59pic10009combination1small2.jpg (118.05 KB, 880x621 - viewed 446 times.) Logged
jehovajah
Global Moderator
Fractal Senior

Posts: 2749

May a trochoid in the void bring you peace

 « Reply #27 on: January 21, 2010, 06:26:31 AM »

Great sequence twinbee. If you look very carefully you will see that surfaces are not being added they are being peeled off. The snow effects represent the layer below that has potential to be shed and the iteration and rules have not defined a stable form. Thus it appears to froth when in fact it is evaporating away in a fog.
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May a trochoid of ¥h¶h iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
twinbee
Fractal Fertilizer

Posts: 383

 « Reply #28 on: January 22, 2010, 07:47:14 PM »

Quote
Makes me want to make thin slices of the last render, with the higest iterations.
I'll see if I can get round to doing that soon - would certainly be interesting!

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Great sequence twinbee. If you look very carefully you will see that surfaces are not being added they are being peeled off.
Hmmm.. are you sure? As far I can see, the surface is only adding material, not peeling away (for example see iterations 7-8 and 16-17).
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LesPaul
Guest
 « Reply #29 on: January 23, 2010, 01:22:54 AM »

Wow!  Does the concept of a "fractional" iteration make sense?  For example, I'd love to see twinbee's sequence of renders made into a movie that evolved smoothly...  but you'd have to be able to render versions at iteration = 9, 9.01, 9.02, etc.
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