DomJustDom
Forums Newbie
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« on: April 14, 2011, 01:48:24 PM » |
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Hi there! I'm just new to the forum and I have a problem. I wrote a Program that displays a 4D-Mandelbrot based on an own Formula. The Forms looked quite beautiful. This Program is not done yet and it's written in OpenGL. Since I'm in an early stage of developing I didn't see much of how the formulas fractal turns out. When I was googling around I found this forum here. I just discovered Mudelbulb and I thought: "Wow what a Program!" But as I asked in meet and greet forums they told me it is difficult to enter an own formula there. That was there: http://www.fractalforums.com/meet-and-greet/hi-and-hello-there-from-germanyBasically the idea of this formula is quite simple: I invented a Complex number j that is j*j=-i. This leads to the Complex number k which simply is k:=j*i. The Formula Z=Z 2+C turns then out this way: | a= | a2 - b2 + 2cd | + a | | bi= | 2ab i - c2 i + d2 i | + b i | | cj= | 2ac j - 2bd j | +b j | | dk= | 2ad k + 2bc k | + c k |
So, anybody there who can convert this, or tell me how to do so? If you got any questions, suggestions, ... feel free to post!  |
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« Last Edit: April 14, 2011, 01:53:29 PM by DomJustDom »
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DarkBeam
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Fractal Senior
Posts: 2512
Fragments of the fractal -like the tip of it
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« Reply #1 on: April 14, 2011, 06:43:10 PM » |
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Hi there. The formula you wrote looks like a quaternion, but some terms look odd, for example that "+a" ... (the final result should be like a normal quaternion in the form z=z*z +z+c or something like) Could you show us a render of your fractal? You can upload images on; www.tinypic.com  |
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« Last Edit: April 14, 2011, 06:46:05 PM by DarkBeam »
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No sweat, guardian of wisdom!
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DomJustDom
Forums Newbie
Posts: 9
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« Reply #2 on: April 14, 2011, 06:55:08 PM » |
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I really really would like to show you a render of this Fractal. (!) But I guess it's not implemented in the standard mandelbulb Program.
The Program I write isn't finished yet. But I'm looking forward to complete it.
Do you know any program where you can write custom formulas?
Or can you create this Formula for mandelbulb or show me how to do so?
In the end, as far as I could see it, it looked like the classical Mandelbrot but in 4D.
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DarkBeam
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Fractal Senior
Posts: 2512
Fragments of the fractal -like the tip of it
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« Reply #3 on: April 14, 2011, 07:20:26 PM » |
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I really really would like to show you a render of this Fractal. (!) But I guess it's not implemented in the standard mandelbulb Program.
The Program I write isn't finished yet. But I'm looking forward to complete it.
Do you know any program where you can write custom formulas?
It seemed that you rendered already something with your new program... Have you got an image, even raw/awful of this fractal?  Yes, it is possible to render it in ChaosPro for example. I am sure that M.Benesi will be happy to help you in a quick code of this formula, good to do a test render of it. I am not expert of Chaos Pro... Basically I hate it  I write formulas for MB3D but since I can not translate every single possible formula for it I need to see an image of it before beginning so if your formula really deserves a translation I will do! Too bad a Mandelbulb formula must be hand coded in assembly so I don't do this if I am not sure of the result |
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No sweat, guardian of wisdom!
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Jesse
Download Section
Fractal Schemer
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« Reply #4 on: April 14, 2011, 10:43:14 PM » |
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i have two questions... | a= | a2 - b2 + 2cd | + a | | bi= | 2ab i - c2 i + d2 i | + b i | | cj= | 2ac j - 2bd j | +b j | | dk= | 2ad k + 2bc k | + c k |
Do you mean + Ca, + Cb i ... at the end instead of + a and + b i ...? And you add + b (or Cb) in line 3 or should it be + c (or Cc)? Same for line 4 but one one character higher. If you want to add C instead, the CommQuat formula is very similar, only some signs seems to be different. greets ps: such simple formulas are not that difficult and time intensive to make for me, in case Luca is overloaded with work  |
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DarkBeam
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Fractal Senior
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Fragments of the fractal -like the tip of it
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« Reply #5 on: April 14, 2011, 11:26:46 PM » |
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If only signs differ, can use scalingplus to fix em? But it screws up +c |
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No sweat, guardian of wisdom!
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Kali
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« Reply #6 on: April 14, 2011, 11:50:32 PM » |
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ps: such simple formulas are not that difficult and time intensive to make for me, in case Luca is overloaded with work Still waiting for that KaliLinComb axis switch  |
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Jesse
Download Section
Fractal Schemer
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« Reply #7 on: April 14, 2011, 11:51:22 PM » |
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Unfortunately the signs differ are only for some parts of the formula, not a whole dimension.
But i tried the formula with C added and it was not very different from the CommQuat formula.
Also the formula with a,b,c and d added showed up some interesting shapes, that might be a nice addition for combinations.
Just Julias won't work without adding C...
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Jesse
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« Reply #8 on: April 14, 2011, 11:55:11 PM » |
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ps: such simple formulas are not that difficult and time intensive to make for me, in case Luca is overloaded with work Still waiting for that KaliLinComb axis switch Huh? Think i have missed something, or i thought an axis switch is not really important  But in the next version i will include the _Flip.. formulas with additional option to switch also C, maybe that can do it? |
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DarkBeam
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Fractal Senior
Posts: 2512
Fragments of the fractal -like the tip of it
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« Reply #9 on: April 15, 2011, 12:07:40 AM » |
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NocJesse it is very important to make hybrids workccorrectly, please  Before beginning to code this formula look if it can be done with my MandyCousin, I am far from my pc now |
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No sweat, guardian of wisdom!
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Syntopia
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« Reply #10 on: April 15, 2011, 12:13:54 AM » |
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Using the following multiplication: vec4 mul(vec4 a, vec4 b) {
return vec4(
a.x*b.x - a.y*b.y - a.z*b.z + a.w*b.w,
a.x*b.y + a.y *b.x - a.z*b.w - a.w * b.z,
a.x * b.z + a.z*b.x - a.w*b.y -a.y* b.w,
a.x*b.w + a.w*b.x + a.y*b.z + a.z*b.y);
}
I got the attached picture (for the Mandelbrot type system, with fourth component = 0) These square Mandelbrots are very similar to the ones you get using Tessarines ( http://en.wikipedia.org/wiki/Tessarine). I might have one or two wrong signs, though :-) |
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Jesse
Download Section
Fractal Schemer
Posts: 1013
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« Reply #11 on: April 15, 2011, 12:18:56 AM » |
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NocJesse it is very important to make hybrids workccorrectly, please Before beginning to code this formula look if it can be done with my MandyCousin, I am far from my pc now The problem with KaliLinComb formula was, that it uses buffers for some axis what makes combinations with other formulas nearly impossible  With the rest of formulas there should be no big problem in combinations |
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Kali
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« Reply #12 on: April 15, 2011, 12:38:30 AM » |
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I got the attached picture (for the Mandelbrot type system, with fourth component = 0) These square Mandelbrots are very similar to the ones you get using Tessarines ( http://en.wikipedia.org/wiki/Tessarine). I might have one or two wrong signs, though :-) That looks definitely like KaliLinComb! I would like to explore the detailed parts closer to confirm that... @Jesse, the axis switch was asked to you by Luca, just for trying to get better combinations with other M formulas. |
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DomJustDom
Forums Newbie
Posts: 9
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« Reply #13 on: April 15, 2011, 01:00:10 AM » |
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Cool, you went on. This looks quite good there, but I meant more this way: | a= | a2 - b2 + 2cd | + aC | | bi= | 2ab i - c2 i + d2 i | + biC | | cj= | 2ac j - 2bd j | +bjC | | dk= | 2ad k + 2bc k | +ckC | | | Zn+1= | Zn | +C |
The idea behind it is simply: j*j=-i j*i=k |
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« Last Edit: April 15, 2011, 01:08:08 AM by DomJustDom »
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Syntopia
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« Reply #14 on: April 15, 2011, 06:50:45 AM » |
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Cool, you went on. This looks quite good there, but I meant more this way: | a= | a2 - b2 + 2cd | + aC | | bi= | 2ab i - c2 i + d2 i | + biC | | cj= | 2ac j - 2bd j | +bjC | | dk= | 2ad k + 2bc k | +ckC | | | Zn+1= | Zn | +C |
The idea behind it is simply: j*j=-i j*i=k I used Z=Z^2+C, together with the multiplication table you posted earlier: R i j k
R +1 i j k
i i -1 k -j
j j k -1 -i
k k -j -i +1
In that table j*j=-1. Knowing how to square a number isn't enough for my approach. I use an analytical distance estimator, which requires multiplication of arbitrary numbers. |
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