Imaginary 3 dimensional Mandelbrot set

[maverdigitalarts]

EDIT 23th, October, 2006:

meanwhile i found another approximation here: http://www.3dfractals.com/

and i tried somewhat in "Processing" http://www.deviantart.com/deviation/41724135/

Still not that what i have drawn.


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EDIT 28th, October, 2006:

New compositions based of my alchemy tries to do 3dimensional mandelbrots......

http://www.fractalforums.com/index.php?topic=233.0
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EDIT 18th, November, 2006:

My code in Processing:  http://www.maverdigitalarts.de/fracts/MultiBrots.pde

[alan2here]

I too am looking for that
best of luck in finding it

[Jules Ruis]

For 3D Mandelbrot set see:

www.fractal.org/Beelden/Mandel.jpg

[Charleswehner]

Unfortunately, what Jules showed you is not actually 3D. It is PERSPECTIVE DRAWING, from a sideways direction.

On my website, I have the original text of Professor Charles Wheatstone, June 21 1838. This was the moment in history when the stereoscope was seen to be invented, and also stereoscopic images.

My preferred method of displaying images in 3D is for "squint" viewing (cross-eyed viewing). One does this for preference in PRIVATE, because a face that is squinting looks silly. Wheatstone himself used the method for his diagrams (at http://www.wehner.org/3d/first/platexi.htm ). The first-ever entertainment 3D image is the arch at the bottom (also shown in the introduction to Wheatstone). I also have some at http://www.wehner.org/3d/towne . The 3D section starts at http://www.wehner.org/3d , where Professor Wheatstone can be seen to wobble as you scroll. This allows "stereoscopy with a single eye", because the 3D effect can be observed even with one eye closed - the kinetic influence on 3D perception is one of my contributions to the science.

So you need TWO images, even if they wobble from one to the other.

I played with the Mandelbrot set, Z <- Z*Z + C, using two different values for C. This is because Mandelbrot is a recursion around the complex numbers X+iY where X is across, and Y is up. Our eyes are side-by-side (in the X axis), so some trick that alters the "perspective" of the Mandelbrot set just by adjusting the X value is needed. Having an interest in mathematics, in graphics and in 3D, I tried it - but nothing was convincing enough to publish.

3D fractal images are indeed a fascinating new field to open up.

Charles

[alan2here]

What we mean charls is that the mbot\juilia\nova ect... sets are all actually 4 dimentional, we can easely desplay them as 2d but we want to represent them as 3d. Ultrafractal and I assume also other software has various ways of desplaying them in 3d (so they can be animation to spin round for example) but all in difrent ways and none in a way that can be agreed is the "correct" way or in a way that looks like how you may imagine it to look like. http://www.deviantart.com/deviation/41353183/

although, heightmaps of the set that are sterioscopic or steriscopic images of the methods can be made, and are intresting to look at.

[Charleswehner]

The way I see Mandelbrot ( Z <- Z*Z + C) is as an iteration using co-ordinates in the complex plane. Z is X+iY where X is the longitude and Y is the latitude. So the plane is a 2-dimensional map.

C is a constant throughout the calculations, so unless one changes the rules of Mandelbrot, it does not give another dimension.

A limit is set for the allowed values of Z, as new Z replaces the old. The count of iterations up to the limit has been used to define the colour (at the "designer's" discretion). It could also be seen to be the height.

I altered C between two images, simply to get a different perspective between the two - hoping to get the complex plane slightly tilted. My "squint" image of a plane is at http://www.wehner.org/3d/towne/trapezia.gif . The further back you sit from the screen, the stronger the 3D illusion. You squint so that the left image is seen by the right eye and vice-versa. When you achieve stereopsis (the double-vision goes, and the image "clicks" into 3d), you see three images. The 3D one is in the middle.

I had not been aware of the abundance of fractal animations until I started exploring this forum. Some of those I looked at showed the "height" as an additional shift in the vertical (the Y axis). Here, the near overwrites the far. When this is animated as a sideways movement, hidden parts of the far image become revealed. This, again, is not 3D. It is changing perspective.

The correct facts about visual perception of 3D are those contained in Professor Charles Wheatstone's paper - which I retyped and put on my site.

However, the kinetic effects of changing perspective were not included in his paper. My "wobbly" Wheatstone is part of that story.

People are quite happy to go to the cinema, or watch television, where the images are 2D because there are enough depth-clues due to changing perspective, and also due to the vanishing point, for most purposes. However, 3D it is NOT. The word 3D has been constantly misapplied by people who really mean perspective.

3D should be a TOTAL simulation of what one sees in real life.

Another factor is peripheral vision (as in Cinerama) - but who can afford the computation-time to create wall-to-wall Mandelbrot?

Charles

[maverdigitalarts]

For 3D Mandelbrot set see:

www.fractal.org/Beelden/Mandel.jpg

Hello Jules,

Thats is a neat approximation, but reminds me of a spinning 2d Mandel ( some lookalike rotation symmetry ).


Greetings,

Marco Vernaglione

[Jules Ruis]

I stay telling you that my image of the 3D Mandelbrot set is a real 3D image. You can believe it or not, but it is!

I produced it as a real 3D with a Rapid Prototyping machine in wax and cintered powder.

[maverdigitalarts]

I stay telling you that my image of the 3D Mandelbrot set is a real 3D image. You can believe it or not, but it is!

I produced it as a real 3D with a Rapid Prototyping machine in wax and cintered powder.

Hello Jules,

Thats quite interesting.



EDIT: 28th, Oct, 2006:

Got somawhat similar here, after experimenting with extentions of the original formula.

Well, the result is a super rotation symmertry mandel... sigh...

in this one i integrated more of these faster escaping points as slices of a solid body.

Instead of prooving if ( aa + bb + cc ) tends to infinity, i set ( aa * bb * cc ) test if it goes to infinity.

The first causes round structures, the second more like the biomorphs in XAOS, its rougher.

[maverdigitalarts]

Unfortunately, what Jules showed you is not actually 3D. It is PERSPECTIVE DRAWING, from a sideways direction.

Hello Charles!

My apologies here, when we say 3d we mean perspective... you know we are computer nerds... and therefore sitting in front of
a 2D screen ;.)


Greetings...

maverdigitalarts