4D Mandelbrot set rotation

[cosmicastaway793]

Ya know, I need a few different 4d structures to represent four major races in possession of higher-dimensional technology situated around the two independently rotating polar regions within a 4-dimensional dyson sphere.

Any cool fractals or tactical structures you could recommend me? Maybe some REAL 3d intersections of a klein bottle instead of the fakey self-intersecting ones so I can reorient 3d spacecraft within 4d space? The 4d mandelbrodt looks like a good start.

[truth14ful]

OK, so is this a 3D slice of a 4D fractal or a 3d shadow of one? And does it have a mandelbrot in 2 dimensions and a julia in the other 2? And can it be rotated in the 4th dimension?

[brian5446]

so the solid grey parts corrispond to the areas where the iterations are bound, or the black parts on the normal graph? If so, why does the graph end? arn't there places of the mandelbrot, no matter where you go, that are bounded and don't iterate into infinity?

[brian5446]

@brian5446 and it is a nice video, im not criticizing, just trying to understand

[brian5446]

so the solid grey parts corrispond to the areas where the iterations are bound, or the black parts on the normal graph? If so, why does the graph end? arn't there places of the mandelbrot, no matter where you go, that are bounded and don't iterate into infinity?

[Whitefire240]

This is god's chandelier.

[jerzkid87]

omg thats the most beautiful form Ive ever seen

[TubeTripping]

So that's how the universe was made...

[starbeline]

So beautiful

[TooMuchToo0ften]

cool!!

[FTpencity]

name of the song? I love it

[thesomeoner]

simply beutiful

what is it... lol

how did you manage to get it in 4D

i can bearly even understand the 4th dimension

[lordjavathe3rd]

nice processing power.

[foxtuba]

The music sounds like some sort of Final Fantasy theme. I like the whole experience, though!

[MarkoJBee]

Nice one Bib!

[MPS186282]

My brain just broke. Brilliant.

[Thepowersurge]

OK, it's beautiful, as are most morphs, quaternion or otherwise.

But what does it mean? I mean, how do you go from pure mathematics to an object that has existence? Or does it?

And, what makes this 4D? A Mandelbrot set is 2D, so an extension along a perpendicular axis, and a subsequent rotation, doesn't that make it 3D? Am I missing something?

[bib993]

@Thepowersurge

In a nutshell, an object is in 4D if it is described by a system of 4 independent coordinates. A Mandelbrot set is 4D if you iterate a function of 4 variables instead of 2 (complex plane).

Displaying a 4D object onto a 2D screen requires a projection. Just like when you display a 3D object onto a screen, you transform 3 coordinates into 2. It's the same with 4 or n, but you lose more information of course.

[kurtilein3]

@Thepowersurge

its one dimension higher, so there are many ways to project a 4 dimensional object into 3 dimensional space, just like there are many ways to project a 3d object into a 2d plane. since you are commenting here, you are probarbly a visual thinker, i recommend the wikipedia-article about hypercube. 2d = square, 3d = cube, 4d = hypercube. or try the 4-dimensional version of rubiks cube, its available online.

[kurtilein3]

@Thepowersurge

one implication... its a 4-dimensional object, but in this video only the 3-dimensional projection is being rotated. you could also rotate in the 4th dimension, then the object would go into a strange, cyclical motion. again, like the animation of the rotating hypercube in wikipedia. it typically looks like the inside of the object is ejected out at some places and the outside sucket in at others, and after a full rotation it always looks exactly like it did at the start.