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16 different spherical coordinate systems 
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#37
Sep509, 10:32 PM

P: 117

See the pictures showing powers 38 from Paul/bugman's site. It also gives the formula directly. http://www.bugman123.com/Hypercomplex/index.html Also see David's ace new animation that morphs between the powers 310: http://makinmagic.deviantart.com/art...irus136033852 Finally, here's a taster of what's to come (with some added shading, but still no where near properly shadowed / globally illuminated / raytraced). Magnification=1284: 


#38
Sep809, 07:06 PM

P: 4,512

After looking at some orbits of the Mandelbrot set using Fractint 20.0, I don't see the nicely behaved orbits I expected. Secondly, I don't think there is any meaningful way to decide which way an orbit should be moving on the next step, or even it's initial direction as you've said.
So givingup on that momentarily, I reexamined the coordinate relationship y:x::y:z and came up with this code.
I haven't tried to see if the Fractint will accept this sort of algorith. 


#39
Sep909, 11:29 AM

P: 117

Hi Phrak, I tested, and the coord system you made is a rotation of the standard 'I' system. I rendered the function anyway. Here's the result:
Interesting about the cranky orbit  I might've guessed. The more I think about it, the more I like your idea to keep trace of the previous/first rotation to see how the next will act. Like you, I hope your fears about it still being ambiguous turn out to be mistaken. Have a look at this shot  it's even more exciting, despite the plain light sourcing: http://www.fractalforums.com/3dfrac...g7910/#msg7910 


#40
Sep909, 10:45 PM

P: 4,512

I shouldn't be too suprised that the result is disappointing. Thanks for posting the results, though. I've learned subsequent to my previous post that Fractint doesn't support 3D fractals in the way we require, so I can't generate any of these myself.
In looking over the code I posted, if the variable c doesn't range, but is set to zero, the mandelbrot set is recovered in 2D. That is, if c is always zero, then z will always be zero. I don't see that in your image. It may be there, but we're looking at it edgeon. I can't tell what view angle you're using, so I don't know if the observer is in the XYplane. In otherwords, as a last resort, I'm hoping you made an error in translating my pseudocode and there's still a chance the 3D factal we're looking for lives in it somewhere. 


#41
Sep1009, 05:39 AM

P: 117

Sorry, there was a mistake. I generally use my own version of sin, cos, atan2 etc. which divide or multiply by pi for convenience, and I changed the sin and cos functions, but forgot to change the atan2 function to my own as well, causing a mismatch.
Here's what we should have seen first time. 3 views this time, with lighter areas at the front. The mandelbrot is sorta there (though not completely?) in the first view: Here's the code for you to check (I tried normal sin/cos/atan2 with exactly the same results). Also I tried squarerooting the r2 variable, but a fuzzy blob came up.
newa = tradd( &(trmultiplyPHRAK(&a)) , &point); 


#42
Sep1009, 07:19 PM

P: 4,512

I take it that the first frame is looking along z into the xyplane. The mandelbrot could be burried behind some overhanging structure. If so, it's esthetically not very interesting overall, but there may be more intersting stuff at higher zooms.
Have you considered how difficult it would be to zoomin on a 3D location? In 2D you can locate a coordinate on the screen. In 3D you don't know where you are without some additional programmingwork to move the mouse in 3D and perhaps highlight things it gets close to. Getting back to your original code where the atan2 function is feed a radius, by a great coincidence, i've been working a problem in differential topology where it is very important that a radial coordinate have an unambiguous positive or negative value. So perhaps if my problem in topology is solvable, it's may be possible to tweek your algorithm to have signed radial coordinates too. 


#43
Sep1209, 07:27 PM

P: 117

http://www.skytopia.com/stuff/mbrot...osssection.png I seem to have found that if it wasn't for the final triplex addition step, the rotation/mulitplication part would be fairly easy to set up to rotate around the sphere in a consistent way. Unfortunately, the addition messes everything up, and ambiguity rears its head. 


#44
Sep1509, 09:12 PM

P: 4,512

By the way, there should also be a 2D mandelbrot in the ZYplane when x is set equal to zero. [/qoute] "Funny you mentioned that  I recently posted about what would be needed at FF. Rather than a camera type zoom (just standard magnification), it would be nice if the camera would instead move in nearer and nearer to the point of interest. As it gets closer to this point, it would need to move slower and slower too. A high angle/field of view would also help create an 'immense parallax/perspective' feel, without the plain orthographic look.[/quote] Yeah. And the software could calculate with a distance measure for the center of field of both near and far surfaces. In this way you could eventually come up with a cubical volume for the next round of iterations. I've been lurking around your Fractal Forum thread. I've discovered that a few ideas I'd had in mind have been worked out already, so instead, I'll be checking the math. That's quite a team youall have goingand two years persistant, at that. Very impressive. 


#45
Sep1509, 09:31 PM

P: 4,512

I just read Wikipedia's long double page.
http://en.wikipedia.org/wiki/Long_double 


#46
Sep2509, 09:04 AM

P: 117

I was using the mingw compiler (through Dev C++). It seems to allow around 1718 significant digits places compared to float (about 8 or 9). Similar results, are achieved through Visual C by the looks of it, though I haven't tried running it through that yet. Maybe mingw is faulty?
For anyone who's interested, I'm a bit excited at the moment (slight understatement, which itself is a slight understatement). Using the original spherical coords formula, but with a higher power, we're producing results like this: Yes, this does seem to be a 'world first'. It's very strange the power 2 version doesn't produce this detail, when higher powers do. 


#47
Sep2509, 09:00 PM

P: 1,705

what am i looking at here?



#48
Sep2509, 09:17 PM

P: 117

Some of the best visuals ever?
Okay let's try again... A tasty gateau, and some romanesco broccoli? Okay, that's not too useful either, let's try once more... A couple of approx *10 scale zooms into a 'true' 3D version of the original 2D mandelbrot, which uses the same principle as the 2D version, but in 3D space. It's not quaternion, as that seems to only produce "whipped cream" style fractals. In summary, it's still not the holy grail I'm searching for, but let's just say I could've been fooled ;) 


#49
Sep2509, 10:27 PM

Sci Advisor
P: 1,593

I would be curious to experiment with some of this sometime. I can code calculations in C easily enough. But what are you using to make the 3D pictures themselves?



#50
Sep2609, 08:22 AM

P: 117

Hi Ben, I had to create my own raytracer for it. I'm fairly lazy (and don't like to reinvent the wheel all the time), so at first I tried looking around at the various 3D software, and asking on various forums, but none of them support rendering of arbitrary 3D functions, at least not functions that can contain while loops and local variables.
The closest I got was maybe Sunflow, Blender or POVray, but in these cases, I'm guessing the speed would suffer drastically (one would need to create a giant voxel array or similar, and it may not support say, shadowing in a practical way again because of speed issues). Your mileage may vary however. 


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