The "3D" 2D Mandelbrot

[Kali]

Hello people.

Someone still searching for the Holy Grail?

I am very excited by this theory:

http://www.fnal.gov/pub/presspass/press_releases/2014/2-D-Hologram-20140826.html

So, we think of extending Mandelbrot fractal to 3D by adding more dimensions...

What about finding a 3D fractal out of the info contained in the original 2D one?

And I'm not talking about the classic height maps.

To be honest, I don't know exactly what I am talking about, really 

Just an idea to work with.

[flexiverse]

From everything I've read I'm sure we live in a holographic simulation.

E.g. http://listverse.com/2013/12/02/10-reasons-life-may-be-a-computer-simulation/

[Kali]

From everything I've read, I'm not completely sure of anything 

[KRAFTWERK]

I love ideas like this one Pablo! ...even if this one even vaguer than my own 

[DarkBeam]

For this idea you deserve a Mandel Box!

[Kali]

 

For this idea you deserve a Mandel Box!

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[Chris Thomasson]

Hello people.

Someone still searching for the Holy Grail?

[...]

What about finding a 3D fractal out of the info contained in the original 2D one?

[...]

FWIW, here is a 3d image created by stacking various poers of the 2d Mandelbrot set:




It just might be of interest to you.

[knighty]

For this idea you deserve a Mandel Box!

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[Chris Thomasson]

Hello people.

Someone still searching for the Holy Grail?

I am very excited by this theory:

http://www.fnal.gov/pub/presspass/press_releases/2014/2-D-Hologram-20140826.html

So, we think of extending Mandelbrot fractal to 3D by adding more dimensions...

What about finding a 3D fractal out of the info contained in the original 2D one?

And I'm not talking about the classic height maps.

To be honest, I don't know exactly what I am talking about, really 

Just an idea to work with.

FWIW, here are some more 3d rendering totally comprised of slices of the traditional 2d Mandelbrot set:

[chronologicaldot]

Not to be a spoil-sport, but 2D information is still 2D information, and I think the whole idea of finding "life is a hologram" is bogus. A hologram in what? Trying to define that would be effectively stripping away the idea of 3D from it's origin, making it totally meaningless.

The idea of finding a 3rd dimension out of 2 means that we're effectively interpreting a new dimension, and there are now limits to said interpretation. For example, the 3rd dimension of a "2D mandelbrot" (a mandelbrot is 2D, lol) could be done in a variety of ways:
a) simply extending the 2D shape along a 3D, perpendicular axis (z)
b) rotating the 2D shape along the axis over which the shape is mirrored
c) multiplying the coordinate values (x and y) by each other (that is: x*y)
d) dividing the coordinate values by each other (x/y or y/x)
e) modulating the coordinate values by each other (x%y or y%x)
f) extruding each point from the 2D plane up by the value of a coordinate (x or y) along the perpendicular axis (z)
etc. etc.

Yes, it's possible to extract a 3rd data value for a coordinate, but it's completely meaningless.

[laser blaster]

My opinion is that there can never be a true 3D Mandelbrot, because fractals like the lathed Mandelbrot and the Mandelbulb already have fractal dimension 3. It's reasonable to guess that a 3D shape where every 2D cross-section has fractal dimension 2 would have to have fractal dimension 4, which is not possible in a 3D space. I don't believe the situation is any better in 4D. So the lathed Mandelbrot is really as fractal as it gets, the trick is to spread the fractal-ness out over all directions so that it looks pleasing to the eye. This is all just a hunch, though.

[cKleinhuis]

i have done exactly the same a few years ago, included in an unreleased mutatorkammer version

the idea was: take an animation and render each frame of an animation as slice, which is not new at all, just rendering a white area from the "inside" of an escape iteration would yield slices for 3d printing

[Chillheimer]

I am very excited by this theory:

http://www.fnal.gov/pub/presspass/press_releases/2014/2-D-Hologram-20140826.html

my personal view is that we live on the fractal boundary between the third dimension - space and the 4th dimension - time.

1d  a line is the infinite to a point
2d  a plane is the infinite to a line
3d  space is the infinite to a plane
4d  time is the infinite to space   
5d  each point in space has an expanding bubble of its own visible universe around it  - and all the points-->bubbles in the kosmos are the infinite to time.

and everything interesting happens between those wholenumbers-dimensions on fractal boundaries.
like our reality between 3d space and 4d time, accurately called spacetime.
or the m-set as a fractal boundary between the first dimension - line and  the second dimension - plane

from this point of view the slicing method sounds reasonable to me. the "3dmset" would be the infinite to each single slice.

my 5 cents..

[Kali]

FWIW, here are some more 3d rendering totally comprised of slices of the traditional 2d Mandelbrot set:

Hi Chris. I was out of the forum and recently came back, I didn't saw your recently posted images. I found this particular ones VERY interesting:



Nice to see how they have Mandelbulb-like features in the 3D surface.

I will be trying your technique myself, I wonder if we can find a DE for this (help anyone?), meanwhile I will use Fragmentarium's NODE-Raytracer.

my personal view is that we live on the fractal boundary between the third dimension - space and the 4th dimension - time.

1d  a line is the infinite to a point
2d  a plane is the infinite to a line
3d  space is the infinite to a plane
4d  time is the infinite to space   
5d  each point in space has an expanding bubble of its own visible universe around it  - and all the points-->bubbles in the kosmos are the infinite to time.

and everything interesting happens between those wholenumbers-dimensions on fractal boundaries.
like our reality between 3d space and 4d time, accurately called spacetime.
or the m-set as a fractal boundary between the first dimension - line and  the second dimension - plane

from this point of view the slicing method sounds reasonable to me. the "3dmset" would be the infinite to each single slice.

my 5 cents..

Yes! that resonates a lot with my own thoughts... thanks for sharing yours