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Author Topic: True 3D mandelbrot type fractal  (Read 374915 times)
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David Makin
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« Reply #165 on: September 04, 2009, 03:51:09 AM »

Quote
@Twinbee - yes, with decreased DE threshold (and maybe increased max. iter.) then the bits will have more bits

Ace, and the romanesco broccoli style veg is the proof by the looks of it smiley Can you render the exact same veg shot again, but with higher iteration / delta DE threshold. Shadows too if poss...

I will, but just at the moment I'm working on code related to my 3D IFS formula - I did the other renders while coding and I haven't expanded the optimised delta DE formula to do shadows or positional lighting yet (that's next on my list, along with moving the rendering into the loop section instead of the global section so that *very* large renders are possible).
I'm just rendering a full-view of the degree 7 version in green at 3000*3000, but still just diffuse lighting.
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bugman
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« Reply #166 on: September 04, 2009, 06:00:45 AM »

I would like to make an animation of the higher power variation of Twinbee's Mandelbrot set, by continuously varying the exponent, but my code is pretty slow. It will take a while for me to complete the render. Perhaps David can render it faster than I could. It seems like his algorithm is quite fast.

Another one I would like to do is show how the 4D version of Twinbee's Mandelbrot set can be continuous animated between different
3D slices.
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David Makin
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« Reply #167 on: September 04, 2009, 12:05:04 PM »

Quote
@Twinbee - yes, with decreased DE threshold (and maybe increased max. iter.) then the bits will have more bits

Ace, and the romanesco broccoli style veg is the proof by the looks of it smiley Can you render the exact same veg shot again, but with higher iteration / delta DE threshold. Shadows too if poss...

OK, no shadows yet though....



Delta DE threshold reduced to 5e-6
As you can see we probably still haven't reached the limit of detail for 256 max. iterations smiley

I haven't uploaded the 3000*3000 render of the whole object as I was disappointed with the result - it most definitely needs better lighting than plain remote diffuse from the viewpoint direction smiley Also I think I overdid the delta DE threshold (at 1e-4) I may try again using say 5e-4.

« Last Edit: September 04, 2009, 12:09:12 PM by David Makin » Logged

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twinbee
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« Reply #168 on: September 04, 2009, 01:04:05 PM »

Wow, it really is beginning to resemble romanesco broccoli, even taking on the IFS look, but of course with a completely different approach.

Can you make the Delta DE threshold lower still (lower = more fine detail right?). I'd love to see even more nooks and crannies... Any chance of 1e-7 or even 1e-8?

Love to see the 3000x3000 1e-4 pic still if you can upload it. Even if it's 'overdone', that may be because of the plain lighting. It will still give an idea of what we can expect once shadows come into play (where I'm guessing no amount of detail can be too fine).
This is really exciting - it's going to look so awesome with full shadowing etc. w00t !!

bugman, I like the sound of animating the exponent!
« Last Edit: September 04, 2009, 02:23:58 PM by twinbee » Logged
David Makin
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« Reply #169 on: September 04, 2009, 08:42:25 PM »

Love to see the 3000x3000 1e-4 pic still if you can upload it. Even if it's 'overdone', that may be because of the plain lighting. It will still give an idea of what we can expect once shadows come into play (where I'm guessing no amount of detail can be too fine).

It was too big for the gallery here, so:

http://makinmagic.deviantart.com/art/Twinbee-s-3D-Mandy-degree-7-135872852
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bugman
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« Reply #170 on: September 04, 2009, 09:26:46 PM »

David, this is astonishingly beautiful.
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Buddhi
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« Reply #171 on: September 04, 2009, 09:41:31 PM »

Yes, this high resolution fractal looks incredible. David, speed of your renderer is really impressive. I think I have to made second separate renderer for fast previews using DE and without rendering slices. Now I have to wait many hours to see any effect.
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twinbee
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« Reply #172 on: September 04, 2009, 09:50:32 PM »

Awesome indeed. Here's another taste of things to come. I took David's previous two images and superimposed them in a special way to imitate light sourcing/shadowing. The real thing should look much better of course!

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David Makin
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« Reply #173 on: September 05, 2009, 07:17:08 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))

I'd be interested to know if anyone can prove that each of the above set of Mandelbrots is connected, actually the same goes for the other "true 3D" version for which I have a suspicion that it may not be connected:

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;
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David Makin
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« Reply #174 on: September 06, 2009, 12:48:43 AM »

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))

I'd be interested to know if anyone can prove that each of the above set of Mandelbrots is connected, actually the same goes for the other "true 3D" version for which I have a suspicion that it may not be connected:

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;


Ooops - make that "for which  I have the suspicion that the standard 3D slice of the 4D set is not connected" which doesn't mean the full 4D object is not connected smiley
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David Makin
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« Reply #175 on: September 06, 2009, 04:04:05 AM »

I would like to make an animation of the higher power variation of Twinbee's Mandelbrot set, by continuously varying the exponent, but my code is pretty slow. It will take a while for me to complete the render. Perhaps David can render it faster than I could. It seems like his algorithm is quite fast.

Another one I would like to do is show how the 4D version of Twinbee's Mandelbrot set can be continuous animated between different
3D slices.


Edit: I updated the animation to a 640*480 version.

Here's an animation of the power varying from 3 to 10:

http://makinmagic.deviantart.com/art/The-Brocolli-Virus-136076770

Anyway rendering 500 frames at 640*480 took 4hrs 34mins, that's around 33 seconds per frame which I think is pretty good for my 2GHz core2Duo laptop in single threaded mode - note that because of the number of higher trig functions involved the core2Duo was actually less than twice as fast as this P4HT at rendering this one.
« Last Edit: September 06, 2009, 02:36:27 PM by David Makin » Logged

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David Makin
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« Reply #176 on: September 06, 2009, 12:26:37 PM »

Here's a zoom into the degree 10 version of bugman's formula:

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twinbee
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« Reply #177 on: September 06, 2009, 01:25:00 PM »

WOW JUST WOW.

 (jaw drops)

How close to the holy grail is this gonna be - the one that I've always been hoping for?! The variety of the shapes is looking so promising! I wonder if the normal version (power 2) has this kind of detail at any point after zooming?

Excellent shot David. You can guess what I'm going to say - I'd love to see a lower threshold for this one cheesy I feel we may be at the point Mandelbrot was when he first discovered the 2D version, but computers took hours or days to render anything.

The animation is also stunning. It's like as if it's trying to subtly force more bulbs on the surface but without losing symmetry.

Quote
I'd be interested to know if anyone can prove that each of the above set of Mandelbrots is connected
I was thinking exactly the same - can't imagine how one might prove it apart from experimentally.
« Last Edit: September 06, 2009, 02:27:45 PM by twinbee » Logged
David Makin
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« Reply #178 on: September 06, 2009, 02:36:56 PM »

I updated the animation to 640*480:

http://makinmagic.deviantart.com/art/The-Brocolli-Virus-136076770
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Buddhi
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« Reply #179 on: September 06, 2009, 04:50:18 PM »

Sometimes ago I made the same with Buddhabrot fractal (power was varying from -6 to to +7). Watch in HD on Youtube:
<a href="http://www.youtube.com/v/KTS7F9dzr4k&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/KTS7F9dzr4k&rel=1&fs=1&hd=1</a>
I think it will be very interesting in 3D. Maybe somebody made some trials with 3D Buddhabrots? I'm planning in near future to write some program for rendering 3D Buddhabrots and animations.
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