David Makin


« Reply #105 on: June 23, 2009, 02:57:30 AM » 




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twinbee


« Reply #106 on: June 24, 2009, 12:15:46 PM » 

With the 3rd dimension thrown in, it's like exploring unchartered space ala Star Trek, all this stuff.
David, I liked the way of demonstrating 3D that those 'sliced' animations used. (Wouldn't mind seeing that one or your latest rendered in Lycium's renderer).



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Buddhi


« Reply #107 on: July 09, 2009, 08:17:04 PM » 

Hello I made some 3D Mandelbrot fractal using David's 4D formula: newx = xx*xx  yy*yy  zz*zz  ww*ww; newy = 2.0*xx*yy + 2.0*ww*zz; newz = 2.0*xx*zz + 2.0*yy*ww; neww = 2.0*xx*ww + 2.0*yy*zz; xx = newx +a; yy = newy +b; zz = newz +c; ww = neww; I rendered this fractal into 3D array: 1500 x 1500 x 1500 pixels and later generate 3D view with some very simple but effective shading algorithm. It takes very huge amount of memory. Only 3,2GB RAM :) but rendering is very fast. It takes only 1 hour to render this. I write my own program in C++ to render this First attached render uses iterations between 15 and 255 to make some "fractal fog". http://www.fractalforums.com/gallery/?sa=view;id=727Second uses iterations higher than 240 and there are visible very sharp shapes. http://www.fractalforums.com/gallery/?sa=view;id=728Thanks Twinbee and David for inspiration. You have done very good piece of work. For more fractals I invite to my gallery: http://picasaweb.google.com/buddhi1980/Fraktale


« Last Edit: July 11, 2009, 08:33:22 PM by Buddhi »

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cKleinhuis


« Reply #108 on: July 09, 2009, 08:26:13 PM » 

wow, the second one is cool, i believe a pertubated mandelbrot .... very nice!



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divide and conquer  iterate and rule  chaos is No random!



David Makin


« Reply #109 on: July 09, 2009, 08:27:15 PM » 

Congratulations on the nice renders ! I'm still hoping that Lycium will have a go at this one using his fractal rendering engine



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David Makin


« Reply #111 on: July 09, 2009, 08:54:57 PM » 

wow, the second one is cool, i believe a pertubated mandelbrot .... very nice!
It's not actually a perurbated Mandelbrot, it does start from (0,0,0,0) but it's using unconventional 4D maths to calculate z^2+c. The maths involved is a 4D commutative ring but not a division algebra and hence not a field. Standard Quaternions are a division algebra but are a noncommutative ring and hence are also not a field. Standard Hypercomplex (sometimes called BiComplex) is a commutative ring but only a partial division algebra and hence again not a field (partial division algebra because not all nonzero values have an inverse).



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bib


« Reply #113 on: July 10, 2009, 03:32:22 PM » 

This last one is very impressive with the red peaks showing the 2D Mset. If you zoom on these, are they completely flat or do they have some thickness with potentielly new fractal shapes ?



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Between order and disorder reigns a delicious moment. (Paul Valéry)



Buddhi


« Reply #114 on: July 11, 2009, 08:50:01 AM » 



« Last Edit: July 11, 2009, 08:39:05 PM by Buddhi »

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Buddhi


« Reply #115 on: July 11, 2009, 08:54:10 AM » 



« Last Edit: July 11, 2009, 08:40:15 PM by Buddhi »

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Buddhi


« Reply #116 on: July 15, 2009, 07:38:01 PM » 

Another view inside 3D Mandelbrot region coordinates: x: 0, 0.5 y: 0.25, 0,25 z: 0.25, 0.25 max iteration number: 256



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stigomaster
Guest


« Reply #117 on: July 17, 2009, 09:03:24 PM » 

Hello guys, I've been keeping an eye on this thread for a little while, although I didn't actually join FractalForums before today. State of the artwork like this is really exciting to watch =) Just a little thought I just got: There is a 4dimensional object, a kind of julibrot, of which the familiar mandelbrot set and julia sets are 2Dslices of, and the quaternion julias are 3Dslices. As we know, the 4th dimension can be thought of as time, and therefore the entire 4Dobject might be presented as an animation of a morphing quaternion julia. In the same way, you can imagine a movie as a 3D object, as a prism where a 2D crosssection is a frame of the movie and the height represents time. But there is only one right direction to play the movie. Taking the crosssections from the side would look completely different. In the same way, how do one know if one is going through the "correct" axis on the 4D julibrot? I kind of think this is relevant to this discussion, although I can not bring you amazing renders. I don't even know if I can render a sphere in POVray without consulting the tutorial



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David Makin


« Reply #118 on: July 17, 2009, 09:28:34 PM » 

Hello guys, I've been keeping an eye on this thread for a little while, although I didn't actually join FractalForums before today. State of the artwork like this is really exciting to watch =) Just a little thought I just got: There is a 4dimensional object, a kind of julibrot, of which the familiar mandelbrot set and julia sets are 2Dslices of, and the quaternion julias are 3Dslices. As we know, the 4th dimension can be thought of as time, and therefore the entire 4Dobject might be presented as an animation of a morphing quaternion julia. In the same way, you can imagine a movie as a 3D object, as a prism where a 2D crosssection is a frame of the movie and the height represents time. But there is only one right direction to play the movie. Taking the crosssections from the side would look completely different. In the same way, how do one know if one is going through the "correct" axis on the 4D julibrot? I kind of think this is relevant to this discussion, although I can not bring you amazing renders. I don't even know if I can render a sphere in POVray without consulting the tutorial Hi, Here's a morphing Julibrot  in this case the 4 fractal dimensions  zstartreal,zstartimag,creal,cimag  are implimented in 3D space by using two of the fractal dimensions directly as 2 spatial dimensions and then using the 3rd spatial dimension as a line in the plane of the 2 remaining fractal dimensions and gradually rotating the angle of this line in this plane by 90 degrees from one of the fractal dimensions to the other, then doing the same with a different spatial dimension:



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stigomaster
Guest


« Reply #119 on: July 17, 2009, 10:01:19 PM » 

HAHA! I commented on that video on YouTube two days ago!



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