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Author Topic: Hi and Hello there from Germany  (Read 1531 times)
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DomJustDom
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Posts: 9


« on: April 13, 2011, 09:44:49 PM »

Hi!

My name's Dom. That comes from the German name Dominik. In Germany this is a male name unlike Dominique in French.
OK, I here because my Hobby is writing Programs. I am familiar with the Mandelbrot fractal, because I often wrote several
programs around that topic. Fractals are a fascinating Thing this is the reason why I joined this Forum.

But, to be honest, I am also here, because I have a Problem, and I need your help.

Once upon a time I thought to myself I did this often enough, and that it would be Interesting to start through in multi-
dimension space. I never heard anything about hyper complex numbers so I started trough with an own formula depending
to Fractals.
A simple conclusion I came to was to develop the next imaginary number j instead of i.
The next thought was why not do the next (-1)-square root within the (-1)-square root.
So the idea was simply to go on that way and to work this out.
(When I go on now I use sqrt() in the sense of a square root.)
So in the end this would lead to the normal imaginary part i (sqrt(-1),
but then to k as the next imaginary number and that would be j as sqrt(sqrt(-1)).
Now it comes to the interesting part k and that is sqrt(-1*sqrt(-1).

To see this in a combination-table it would look like this:

Rijk
R+1ijk
ii-1k-j
jjk-1-i
kk-j-i+1

Then I did Zn+1=Zn+C, and it seemed to turn out as a 4D-Mandelbrot.
I googled a lot, but I didn't find this Form in the Internet, since these Forms look beautiful,
as far as I could see them. Well to be honest, I didn't see that much yet, because I'm still working
that program out. Does anybody of you know how this Form is called, and where to find more around that topic?
« Last Edit: April 13, 2011, 10:03:08 PM by DomJustDom » Logged
Fractal Ken
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« Reply #1 on: April 13, 2011, 10:35:31 PM »

Welcome, Dom! You've come to the right place for discussing 3D and 4D fractals.

The number system you're exploring appears similar to quaternions, which are often used in generating fractals.

Note that the square root of i, that is, sqrt(sqrt(-1)), exists within the complex numbers. It is plus or minus (1 + i)/sqrt(2).
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cKleinhuis
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« Reply #2 on: April 13, 2011, 10:57:00 PM »

hello and welcome, you will then find the triplex method very interesting smiley
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DomJustDom
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Posts: 9


« Reply #3 on: April 13, 2011, 11:47:15 PM »

Thanks for everything that far! I really feel welcome here. happy
I just downloaded the Mandelbulb Program. Is there a manual somewhere in this Form.
I'm new here and I didn't find it yet.
Just some way to hack in a Formula on my own.
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Sockratease
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« Reply #4 on: April 13, 2011, 11:52:26 PM »

Hello and Welcome   afro

There is really no manual for Mandelbulb 3D of which I am aware, but it's pretty easy to get the hang of, and if you have any specific questions just ask in the Mandelbulb 3D section of the forum!  (found here:  http://www.fractalforums.com/mandelbulb-3d/ ).  The creator of the program (Jesse) and many others are available to help with problems.
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Kali
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« Reply #5 on: April 14, 2011, 05:50:41 AM »

Welcome to FF, Dom!

You can ask Jesse, but also look for Darkbeam (Luca), he is a patient in a mental institution but he can help you anyway into making some modifications to the formulas. There is not a direct and easy way for implementing a formula of your own with Mandelbulb 3D, sorry.

P.S.: Just kidding about the mental institution (I think), but he is crazy enough to understand and modify hundreds of complex fractal formulas and transforms from a program he didn't wrote and that were already compiled into assembly code wink
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DomJustDom
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Posts: 9


« Reply #6 on: April 16, 2011, 03:11:47 AM »

Hi again!

I'm getting into it right now, the Forum is really the right place to hang around.
Thanks to Kali and Jesse I had contact to Darkbeam and Jesse.
Woohow, they are really upfront.

Since I'm a newbie it to some time to figure out the right formula tables, but this should be the final version.

The idea is still simple:
j*j is -i
and j*i is k

This was the original idea behind it, so forget about the sqrt(-1*sqrt(-1)). I guess this wasn't it.

So the combination table looks like this:

*1ijk
1+1+i+j+k
i+i-1+k-j
j+j+k-i+1
k+k-j+1+i

I guess this is a modified quaternion as far as I understood it. But in case one of you has an more in depth description for this, or a place in the forum to ask for this, pleas let me know.

In the end this is a 4-dimensional fractal, so I called the variables a,b,c and d.
But I wanted a Mandelbrot-Style structure so I have to do the Zn+1=Zn2+C with the quaternion.

In the end the Zn*Zn multiplication table looks then like this:

*a1bicjdk
a1+ a2 1+ ab i+ ac j+ ad k
bi+ ba i- b2 1+ bc k- bd j
cj+ ca j+ cb k- c2 i+ cd 1
dk+ da k- db j+ dc 1+ d2 i

Last step: sorting out and rearranging.

The final formula looks this way:

an+1    =  + an2   - bn2   + 2cndn          + aC
bn+1 i  =  + 2anbn i - cn2 i + dn2 i        + bC
cn+1 j  =  + 2ancn j - 2bndn j        + cC
dn+1 k  =  + 2andn k + 2bncn k        + dC

By the way, someone appeared in the http://www.fractalforums.com/mandelbulb-3d/new-to-madelbulb-can-sombody-help-me-with-a-formula/ topic and told something about the "holy grail". Can anyone tell me what this is about and where to find it?

So far so good.
Basically I'm still looking for mistakes in the Formulas and that.
So corrections, suggestions, etc ... are welcome!

Greetz
   Dom
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David Makin
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« Reply #7 on: April 16, 2011, 04:23:48 AM »

Hi Dom,

The most relevant thread with respect to the "holy grail" is probably what I call simply *the* thread and I guess you've probably noticed it already because it's got a *very* high view count !!
It's this one:

http://www.fractalforums.com/3d-fractal-generation/true-3d-mandlebrot-type-fractal/

There's no perfect definition for the "holy grail" AFAIK, everyone has their own idea but generally the "holy grail" would be a 3D+ version of the z^2+c Mandelbrot that has fractal dimension/self-similarity in all directions within it's dimensionality i.e. you can't find a "straight" line drawn on the surface *anywhere* that doesn't exhibit fractalness smiley To put it another way - simply the fractal has no "whipped cream".
As many have said this is probably impossible due to the abscence of conformity in 3D+ with respect to power functions (I think conformity is the correct term, my higher math is not "formal").
For me as far as the "holy grail" is concerned I'd go further and say it would be a 3D version of z^2+c where the X-Y and X-Z 2D slices are identical and both identical to the standard complex (2D) Mandelbrot and the entire fractal has 90 degree symmetry around the x- axis and the 2D slice in the y-z through the top/bottom/front/back bulbs would look like this:

      o
   o O o
      o

Where the capital O is the cross-section of the main period 1 cardioid and the smaller o's are cross-sections of smaller bulbs that are virtually spherical in 3D (and of course the o's and O should be touching).

And obviously the end of the Set to the negative x would be "pointy" and to the positive x would be "roundy" wink
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