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Author Topic: Implementation: 3D mandelbrot type fractal  (Read 64408 times)
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KRAFTWERK
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« Reply #15 on: May 31, 2010, 04:47:32 PM »

Hi and sorry if I'm interrupting a specific project here.  This is something different.  I've been having a dialogue principally with Jehovajah in "...search for the holy grail continues..." section, and am convinced there is an implementation problem for one approach to M in extended Dims.  I'd love to get more to look at the ideas I'm trying to communicate there. Taken together, the messages I left are enough to duplicate my 2-d results and judge whether a 3-d generator for it exists or can be written easily.  My comments begin on page 12 and continue to the present.  Would love to show some pix, make a paper available, and provide my formula files for this in FractInt.  Someone please advise.

You should try Subblues pixelbender-script (that is the renderer I use).
It is possible to change the formulas in the script, so you might be able to implement your new formulas in it.
Pixelbender is a free Adobe-app (Win&Mac), you can download it here:
http://www.adobe.com/devnet/pixelbender/

Subblues script for it is here:
http://www.subblue.com/projects/mandelbulb

I hope this helps!

J
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fracmonk
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« Reply #16 on: May 31, 2010, 08:24:59 PM »

K- Wow, so fast!  Not used to that.  If I could upload the stuff mentioned, you'd see it's no more complicated than the math principles that gave us complex nos. in the first place. (Honest!) But I do need to do that still.  I'm a babe in the woods when it comes to telecommunications, oddly enuf, so I need that kind of patience!  Anyway, don't know if I'm missing something, but I haven't found anything in "help" here about how to do that.  Thanx!

Didn't realize this thread spilled onto a second page already.  Went to pixel bender, and it's like learning another language, "easier than C++", but it looks nearly as involved.  In the bad old days, I did this stuff in BASIC.  Miserably slow by today's standards.  If I was to invest that kind of time, + I think I will eventually have to break down and do that, I'd go to C++ for versatility in other areas.  Still, I see the results.  Neat!  Another issue w me is having witnessed the evolution of fractal art obscuring the basic math for those inclined to understand it.  I would never ever do that, having been too frustrated over the years w people who seem to go out of their way to make things hard to grasp.  It may be formality, but it presents hurdles unnecessarily, in my humble opinion.  If something could be made plainer, it ought to be.
« Last Edit: May 31, 2010, 08:43:01 PM by fracmonk, Reason: more » Logged
KRAFTWERK
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« Reply #17 on: June 01, 2010, 08:48:57 AM »

Going a bit off topic here I guess... But I share your interest in the basics of fractals, the plain mandelbrot set is for me far more beautiful than much of the "fractal art" some people call fractal...

That is why I try to do plain mandelbulbs (with some experimental exceptions wink ) And look forward to the next step closer to the "real" 3D mandelbrot.

Keep on searching fracmonk! I hope you find a tool that suits you, I'd love to see some renderings!
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fracmonk
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« Reply #18 on: June 01, 2010, 02:37:32 PM »

K- I can't see how it's off-topic at all.  As far as I can see, this is the basic M in an extension environment that is meaningful to both the mathematics of complex numbers and the the famous function we have come to love.  That 2-d slice that Dr. M came up with circa 1980 just happens to have its characteristics because the set of complex nos. is the smallest CLOSED set of 2^n dimensions (n being a pos integer).  But we can look at it from other helpful points of view.  My "grail" has been to provide new insights for others with greater skill and understanding of the MLC conjecture and the very concept of local connectedness than I have.  From what I've read, even Dr. M himself has trouble with the distinction between M's simple connectedness and the possibility of its local connectedness.  I must leave it to people who have reason to believe they have a deeper grasp of the topological distinction, if any truly exists.

Now THAT's off-topic!  But it's still relevant, as mathematics is supposed to seek truth.

ON topic: So far, the .frm file for FractInt I left in the "grail" thread is a good 2-d implementation, and if no existing prog can display it in more dims, one would have to be made.  (If it means that much to anyone- I think it's important in ways others don't yet see) Give that paper a read, and you'll see what I mean.  To understand the underlying math is well worth the effort.
« Last Edit: June 02, 2010, 12:56:25 PM by fracmonk, Reason: fix itses, etc » Logged
fracmonk
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« Reply #19 on: June 02, 2010, 01:14:51 PM »

Having the luxury currently to look around a little bit, if implementation means finer points of using existing progs, this deal should move to "programming" section properly.  Yes?  No?

Still think it's worthy of more eyes upon it.  Also, I might add that proper overviews of a multidimensional object require enormous numbers of pictures (for instance, 4 x 3-d ANIMATIONS with undisplayed 4th dimension as the frame-by-frame (time increments) in this 4-d case) to do them justice, and I don't want to hog space, even w 2-d renderings.  Besides, d.i.y. is very fulfilling.  "Use the formula file, Luke!" said Obi... (before anyone jumps to conclusions, I'm not a big StarWars fan, but the quote seemed fitting)  Be well!
« Last Edit: June 02, 2010, 02:02:50 PM by fracmonk » Logged
KRAFTWERK
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« Reply #20 on: June 02, 2010, 01:19:01 PM »

(for instance, 4 x 3-d ANIMATIONS with undisplayed 4th dimension as the frame-by-frame (time increments) in this 4-d case) to do them justice...

That sounds inqredible interesting, I hope someone here with the knowledge will do that some day!

I downloaded your paper, will see if I can grasp it...   afro
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fracmonk
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« Reply #21 on: June 03, 2010, 03:24:18 AM »

K- Happy to hear that.  Please critique on clarity if you will.  I wanted it to be as easy to follow as possible.  Thanx!  And of course, if you need further explanation, there are no stupid questions...


* 2of4Daxb.GIF (9.71 KB, 320x200 - viewed 2236 times.)

* 2of4Daxd.GIF (8.61 KB, 320x200 - viewed 2207 times.)

* 2of4Daxc.GIF (8.94 KB, 320x200 - viewed 2180 times.)
« Last Edit: June 04, 2010, 03:31:22 AM by fracmonk » Logged
fracmonk
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« Reply #22 on: June 04, 2010, 03:36:30 AM »

Here are 2-d's with other two dims=0 as basics which would call up the right formula files in FractInt to zoom or change param settings, here and in the previous post (modified, and if it works...)

In last post, the first will be very familiar.  The rest will recombine dimensions, this one w that one, taking turns.  With 4-d objects, taking turns is the thing, since it's just not visible all at once, or displayable all at once, but curiously, all dimensions can be combined seamlessly just the same (as long as they...take their turns...)  At first glance, not terribly exciting, but you 3-d ray-tracer types can cure all that!


* 2of4Dbxc.GIF (11.55 KB, 320x200 - viewed 2296 times.)

* 2of4Dbxd.GIF (8.01 KB, 320x200 - viewed 2157 times.)

* 2of4Dcxd.GIF (7.53 KB, 320x200 - viewed 2203 times.)
« Last Edit: June 04, 2010, 03:48:37 AM by fracmonk, Reason: explain attachmts » Logged
fracmonk
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« Reply #23 on: June 11, 2010, 12:43:20 PM »

I may have misled some of you w the last 2 posts a bit.  The pix need the .frm file that made them, which can be found in the "search for the holy grail continues" thread.  It must be present to do any changes to them.  Sorry if I caused any undue frustration.

There was a glitch in the code that made these, found only yesterday (11-11-10).  The correct code for the right images, a bit different, can be found at post 251 in the aforementioned thread.
« Last Edit: November 12, 2010, 05:18:15 PM by fracmonk » Logged
jehovajah
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« Reply #24 on: July 01, 2010, 09:13:27 AM »

@Fracmonk, now i see your pics i am fairly convinced that Quasz has it right. When i get time i will render the variation using the k unit vector to see if it matches the other 3 images you have produced.

The problem as always is one of perspective and technique and settings. The 3d view has to make certain assumption to compute a surface,and then to colour it. David Makin i am sure can take you through the theory of that, but it means that an object can look very different in renders with different settings: thus the mandelbrotp settings are closer to what you are getting than the mandelbrot settings, in Quasz that is. Good luck and good fortune!
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fracmonk
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« Reply #25 on: July 02, 2010, 06:42:00 PM »

J- Kinda heard that before, but never saw a silhouette that matched unequivocally yet.  Saw some slick (OK, really slick) pix in gallery showing very impressive 3d stuff- lighting, colors, intonations, etc.  I'm afraid most are too hypnotized with polish to pay much attention to the math anymore.  I mentioned at the "grail" thread how i'd kinda like to see someone try it my way, duplicate my results, and do their own survey in 2-d before evaluating whether QuasZ can really do it.  If it could, I'd buy it!  But to be honest, in a perfect world, the math behind these pix should have showed up before quaternions did.  The world, however, is never that way, is it? 
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Alef
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« Reply #26 on: December 08, 2011, 04:27:52 PM »

Well, continiuing with http://www.fractalforums.com/3d-fractal-generation/true-3d-mandlebrot-type-fractal/ I was trying to implement true mandelbrot in 3D.

I think, mandelbrot set is generated becouse in complex numbers x^2 = real^2 >< y^2 = i^2. So mandelbrot set is property of numbers themselves and not of the simple formula z=z^2+c.

In quaternion numbers still x^2 >< y^2. But I think z^2 = j^2     =    y^2 = i^2. So correct z^2  allways will be eather x^2 or y^2 or n*y^2. Square have just two posibilities + or -. So by having equal values at z and y axis it generate rotation surface. Unless numbers are being manipulated so that x >< y >< z wink

But if you iterate:
z= quaternion ( real(z) , imag(z), part_j(z)+ part_k(z), part_k(z) - part_j(z) );
z= z*z+C;

It still have features of rotation surface / being extruded but it gained fractal features in z axis and zooming in reveals more features. In 2D it generates unaltered mandelbrot set. j+k and k-j are just try and error...

However, there would be matematicaly corect 3D Mandelbrot set, probably it woun't reveal so nice images as mandelbulbs, since tentacles would go in all direction, creating chaos;)


* 3Dmandelbrot_zoomedin.jpg (197.83 KB, 800x600 - viewed 1486 times.)

* 3D_mandelbrot_manipulated.jpg (74.89 KB, 600x467 - viewed 1467 times.)
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« Reply #27 on: August 21, 2016, 12:13:13 AM »

that one is my favorite fractal I all so like IfS types to  Cantor Dance A peacock
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