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Author Topic: True 3D mandelbrot type fractal  (Read 419903 times)
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Buddhi
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« Reply #270 on: October 03, 2009, 03:55:46 PM »

Wow! Wonderful rendering! Lycium, did you render this using raytracing with radiosity? Final effect is amusing. It is worth waiting for it whole day.
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lycium
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« Reply #271 on: October 03, 2009, 04:02:13 PM »

thanks smiley yes, it has global illumination with unlimited number of light bounces. the fractal iteration is done in double precision to 8 iterations, so it takes a very long time to compute!
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David Makin
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« Reply #272 on: October 04, 2009, 02:01:57 AM »

finally, after a day of rendering:

I couldn't resist doing something similar, so here's a slightly different view of a very simple crater lake but just plain Phong using 2 remote light sources - one to get the shadows and the other a source from the camera direction to get pseudo-global illumination.

Resized to 1280*960 from the original rendered on my 3GHz P4HT in double-threaded mode @3840*2880 in 3hrs 7mins.



If no image above or to see the full 1280*960 version then go here:

http://makinmagic.deviantart.com/art/Crater-Lake-139108178

« Last Edit: October 04, 2009, 02:23:23 AM by David Makin » Logged

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twinbee
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« Reply #273 on: October 04, 2009, 02:56:33 PM »

Good stuff above - like the perspectives.

Karl, you posted the below earlier on in the thread - do you know the equivalent for the power 3 formula?

Quote
if( abs(y) < really_small_value )
newx = x*x-z*z
newy = 0
newz = -2*z*sqrt(x*x)
else other code
« Last Edit: October 04, 2009, 05:05:16 PM by twinbee » Logged
bugman
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« Reply #274 on: October 05, 2009, 05:17:14 AM »

Here is an animation of my 4D variation of Twinbee's formula. It looks like some sort of a spaceship to me:
http://bugman123.com/Hypercomplex/Mandelbrot-White4D.m1v
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Karl131058
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« Reply #275 on: October 05, 2009, 08:49:02 AM »

@twinbee:

Hi Dan,

Thats easy to do:
To get rid of that not-really-existing pole on the z-axis you simply set y=0 in the formulae,
that gives:
if( abs(y) < really_small_value )
   newx = ( x^3 - 0 ) * ( 3*z^2 - x^2 - 0 ) / ( x^2 + 0 ) = x*( 3*z^2 - x^2 )
   newy = 0
   newz = z * ( z^2 - 3*x^2 )
else
   (other formulae)
endif

That's all...

Hope that helps, have fun

Karl
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bib
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« Reply #276 on: October 05, 2009, 08:32:01 PM »

Here is an animation of my 4D variation of Twinbee's formula. It looks like some sort of a spaceship to me:
http://bugman123.com/Hypercomplex/Mandelbrot-White4D.m1v


is it a bird is it a plane?
Nice work smiley
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David Makin
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« Reply #277 on: October 05, 2009, 11:10:25 PM »

Hi all, finally got around to being patient enough to get a pretty decent animation of the degree 4:

<a href="http://www.youtube.com/v/hwnAKFlXmtA&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/hwnAKFlXmtA&rel=1&fs=1&hd=1</a>

Hope you like it - it took aaround 55 hours to render (500 frames @640*480) on this decrepit 3GHz P4HT.

Apologies for the odd error here and there - and for the aliasing - I plan on doing a re-render at work on Steve's MacPro @1280*960 with the "accuracy" setting increased - to be resampled down to 640*480.

Am working on my WIP formula adding extra (simple) objects to go in the background to act as shadow receptors and/or mirrors.
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David Makin
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« Reply #278 on: October 05, 2009, 11:19:27 PM »

Here is an animation of my 4D variation of Twinbee's formula. It looks like some sort of a spaceship to me:
http://bugman123.com/Hypercomplex/Mandelbrot-White4D.m1v


Hi Paul - is that animated by just varying the 4th dimension coordinate ? If so you may get a more interesting animation by rotating the 3rd spatial axis as a line from the 3rd fractal axis to the 4th fractal axis (i.e. as a line in the j,k plane through 90 degrees from the j axis to the k axis).
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bugman
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« Reply #279 on: October 05, 2009, 11:54:42 PM »

Here is an animation of my 4D variation of Twinbee's formula. It looks like some sort of a spaceship to me:
http://bugman123.com/Hypercomplex/Mandelbrot-White4D.m1v


Hi Paul - is that animated by just varying the 4th dimension coordinate ? If so you may get a more interesting animation by rotating the 3rd spatial axis as a line from the 3rd fractal axis to the 4th fractal axis (i.e. as a line in the j,k plane through 90 degrees from the j axis to the k axis).

It is a 3D "slice" of the 4D object starting from w=0, and then rotating to z=0, then rotating to y=0, then rotating to x=0, and finally rotating back to w=0 again.
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David Makin
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« Reply #280 on: October 06, 2009, 12:00:55 AM »

Here is an animation of my 4D variation of Twinbee's formula. It looks like some sort of a spaceship to me:
http://bugman123.com/Hypercomplex/Mandelbrot-White4D.m1v


Hi Paul - is that animated by just varying the 4th dimension coordinate ? If so you may get a more interesting animation by rotating the 3rd spatial axis as a line from the 3rd fractal axis to the 4th fractal axis (i.e. as a line in the j,k plane through 90 degrees from the j axis to the k axis).

It is a 3D "slice" of the 4D object starting from w=0, and then rotating to z=0, then rotating to y=0, then rotating to x=0, and finally rotating back to w=0 again.


Oh ! OK - I guess I should have investigated first smiley
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David Makin
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« Reply #281 on: October 06, 2009, 12:37:26 AM »

OK I confess there was another major oversight in my delta DE pseudo-code which I have now corrected:

http://www.fractalforums.com/3d-fractal-generation/true-3d-mandlebrot-type-fractal/msg7812/#msg7812

Basically the newly calculated step distance (Directional DE/scale) needed to be assigned to the "step" variable - my apologies to those trying my code !
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bugman
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« Reply #282 on: October 07, 2009, 05:49:48 PM »

Here are some higher power variations of Twinbee's Mandelbrot set using the following formula:
{x,y,z}^n = r^n{cos(n*theta)cos(n*phi),sin(n*theta)cos(n*phi),-sin(n*phi)}
r=sqrt(x▓+y▓+z▓), theta=atan(y/x), phi=atan(z/sqrt(x▓+y▓))

These higher order 3D Mandelbrot sets were created using the same formula as above, except the sign of the z-component is switched (the rotation about the y-axis is reversed):
{x,y,z}^n = r^n{cos(n*theta)cos(n*phi),sin(n*theta)cos(n*phi),sin(n*phi)}
r=sqrt(x▓+y▓+z▓), theta=atan(y/x), phi=atan(z/sqrt(x▓+y▓))


* Mandelbrot-WhiteNz.jpg (130.07 KB, 556x371 - viewed 863 times.)
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David Makin
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« Reply #283 on: October 07, 2009, 06:45:56 PM »

A deeper look at the degree 7:



If no image then go here:

http://makinmagic.deviantart.com/art/Bridges-139503621
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twinbee
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« Reply #284 on: October 07, 2009, 07:21:48 PM »

Like the anim! (still want a zoom in tho). Interesting image too - didn't realise there were big gaping holes in the object as shown. Curious...

Lycium, is that a special kind of lighting used to create the more 'polarized' look (black/white), rather than for more grey shades?

It'll be interesting to see some (apx.) pow 20 renders of this thing cheesy
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