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Author Topic: True 3D mandelbrot type fractal  (Read 355466 times)
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bugman
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« Reply #225 on: September 24, 2009, 07:07:32 AM »

Wow Twinbee, I couldn't see your fractal renderings until now because I was at work. Those really are stunning. How long did they take to render and how many samples are you using per pixel for anti-aliasing?
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twinbee
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« Reply #226 on: September 24, 2009, 10:01:33 AM »

Thanks, love the julia renderings you and David are making too.

The first took around 1 to 2 days as far as I know. It used no antialiasing at all (apart from for the forum preview, which was scaled down from 2000x2000 to around 770*770.

The second one took about 6-12 hours, and also had no anti-aliasing (apart from a minimal scaling from 800x800 to 770x770 which blurs it a bit). In addition, it was given no justice. Here's a 2000x2000 which is better, not least because an extra couples of valuable iterations were also used (8 instead of 6 - makes all the difference):

"Fractal Foliage".

No anti-aliasing for this either. It does need it, so I'm doing a monsterous 4000x4000 version now. Should only take a week or so grin

Interestingly, a hundred iterations produces very interesting results (I'll post something soon). Thanks to the shadows, they're not so bitty as one might expect, though they're not as smooth as the lesser iterations, unless we go for massive oversampling/anti-aliasing!

« Last Edit: September 24, 2009, 11:50:59 AM by twinbee » Logged
cKleinhuis
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« Reply #227 on: September 24, 2009, 02:38:23 PM »

i am going to set up a gpu renderer for that ... and try to make it as a benchmark or windows screensaver for current graphics cards ... yummy yummy
 evil wink afro afro afro
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bugman
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« Reply #228 on: September 24, 2009, 06:24:47 PM »

i am going to set up a gpu renderer for that ... and try to make it as a benchmark or windows screensaver for current graphics cards ... yummy yummy
 evil wink afro afro afro

I would like to see that. I wish I knew how to program the GPU. You can animate the inverse method in real time.
« Last Edit: September 24, 2009, 06:27:52 PM by bugman » Logged
Rudy
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« Reply #229 on: September 24, 2009, 06:31:20 PM »

Good going, Twinbee, that shadowed 8th degree polynomial 3D Mandlbrot-like set is the best yet.  I like your line,

"In the gateaux pic, imagine standing on one of the 'balconies' and looking across and down the surface on the mountain, with sumptious detail to either side."

People sometimes ask why the 3D 'brots don’t have the color bands like in the 2D mandelbrot ... it's because everything we see in these images has the same escape iteration count…the visible pixels are all on the surface. But the shadowing gets a lot more kapow from the 3D.

 In a better world, we could make the pixels translucent to varying degrees, and have the 100 step iteration faintly visible as purplish fingers inside the pale gold of the ten step iteration, and so on.  Like a translucent Cthulhu cuttlefish.

For now I just wish I go in there and fly around.  To that end, I'm actually including a scene like this in an SF novel I'm currently writing.  Your work is an inspiration.

I say a little more about this in a more recent blog post http://www.rudyrucker.com/blog/2009/09/21/breaking-the-bank-of-computation

"Down inside one of those craterlike holes, off a balcony a third of the way up , down a spiral hallway, with everything steadily shifting its shape and fresh doorways opening up, tunnels closing off, everything translucent with deep shades of color within, the Mathematician is waiting for SOMETHING, it's hard to be sure what---he image of his lost love? A shape so hideously eldritch as to enrage the great Mind of Flimsy itself?"


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David Makin
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« Reply #230 on: September 24, 2009, 09:02:17 PM »

i am going to set up a gpu renderer for that ... and try to make it as a benchmark or windows screensaver for current graphics cards ... yummy yummy
 evil wink afro afro afro

Christian I don't suppose you have a small sample project using shader 2 under DirectX say to render a 2D Mandy or Julia ?
I only have an ATI X600 at the moment and would like to do something with that - initially just 2D fractals.
I found this code: http://files.myopera.com/nerius/files/GpuFractals.zip but it's for shader 3, is it possible to do something similar under shader 2 ?
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cKleinhuis
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« Reply #231 on: September 24, 2009, 09:10:36 PM »

i did a fractal 2d renderer und shader1.0 smiley
but i suppose it is a bit hard to realize 3d rendering under shader2.0 hardware ...
i even can not get it running under 3.0 hardware right now...  cry
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David Makin
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« Reply #232 on: September 25, 2009, 01:11:06 AM »

While everyone's rendering these at higher zoom, you may like to try some quality renders of the (approx) degree 4 version:

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twinbee
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« Reply #233 on: September 25, 2009, 03:55:44 AM »

Quote
In a better world, we could make the pixels translucent to varying degrees, and have the 100 step iteration faintly visible as purplish fingers inside the pale gold of the ten step iteration, and so on.  Like a translucent Cthulhu cuttlefish.

Hey I thought of that too - good idea! I have almost zero idea how that would look, but it could only look incredible. Though it would kill all CPUs dead heh. Also a mirrored surface, or deep refractive index to make the mountain like a crystal would look awesome I bet. Did you real my earlier post about coloring each pixel as an average of the colours of the voxels within a specified radius from that initial/voxel? (Duncan's idea).

Quote
For now I just wish I go in there and fly around.

Wow, yeah me too! Wouldn't that just be so cool. Also zooming the camera into the neverending structure (with full perspective could look amazing).

And that's just the beginning, one could travel inside the object, or any one of its nooks and crannies like you were saying. I should try to 'chop' a layer of the gateau mountain off to see if there's holes inside wink

Quote
While everyone's rendering these at higher zoom, you may like to try some quality renders of the (approx) degree 4 version:

I wonder if zooming into the degree 3 version will exhibit amazing detail like degree 8.

Trifox, GPU rendering for this would so awesome! I wonder how suited they are to using sin and cos with double precision numbers etc.
« Last Edit: September 25, 2009, 04:30:27 AM by twinbee » Logged
David Makin
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« Reply #234 on: September 25, 2009, 12:31:27 PM »

<snip>
Trifox, GPU rendering for this would so awesome! I wonder how suited they are to using sin and cos with double precision numbers etc.

As far as I am aware float is still the highest precision available on GPUs - this is the reason I'm saving for my dream MacPro with Dual Quadcore Nehalems rather than going for something with lesser CPU/s and ultimate video card.
However I am definitely going to play around with GPU programming - starting on the new iPhone/iTouch devices - I'm even going to go into "work" on Saturdays to do it ! (Unfortunately Steve won't let me take one of Parys Technografx' Mac minis home).
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lycium
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« Reply #235 on: September 25, 2009, 02:28:13 PM »

As far as I am aware float is still the highest precision available on GPUs - this is the reason I'm saving for my dream MacPro with Dual Quadcore Nehalems rather than going for something with lesser CPU/s and ultimate video card.

from http://techreport.com/articles.x/17618/5 -

Quote
Demers claims the GPU is compliant with the IEEE 754-2008 standard, with precision-enhancing denorms handled "at speed." The chip now supports a fused multiply-add instruction, which takes the result of a multiply operation and feeds it directly into the adder without rounding in between. Demers describes FMA as a way to achieve DP-like results with single-precision datatypes. (This FMA capability is present in some CPU architectures, but isn't yet built into x86 microprocessors, believe it or not—though Intel and AMD have both announced plans to add it.)
Quote
The Radeon HD 5870's peak processing power is formidable at 2.7 TFLOPS for single-precision math and 544 GFLOPS for double-precision.

what we're all REALLY waiting for is intel's larrabee smiley


right now i'm rendering one of these generalised julia sets, they are amazing! from my previous experiences with generalised julia sets the most interesting ones had a rational exponent p/q with p and q relatively prime; this introduces an element of periodicity when iterated that produces marvelous repeating patterns.
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bugman
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« Reply #236 on: September 25, 2009, 06:07:45 PM »

Quote
In a better world, we could make the pixels translucent to varying degrees, and have the 100 step iteration faintly visible as purplish fingers inside the pale gold of the ten step iteration, and so on.  Like a translucent Cthulhu cuttlefish.

Aren't translucent pixels the same thing as the volumetric approach that Buddhi and I rendered?

Regarding refraction and dispersion, here's part of one I rendered over a month ago. But I didn't finish the render because I wasn't satisfied with the results.


* dispersion-small.jpg (47.58 KB, 280x280 - viewed 2100 times.)
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bugman
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« Reply #237 on: September 25, 2009, 09:17:41 PM »

I attempted to implement David Makin's fast method for distance estimation. I kind of understand how it works but not exactly, and it's giving me weird results. It seems to be about 5x faster, than my regular method.


* MakinsMethod.jpg (135.95 KB, 563x282 - viewed 2151 times.)
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David Makin
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« Reply #238 on: September 25, 2009, 10:16:48 PM »

I attempted to implement David Makin's fast method for distance estimation. I kind of understand how it works but not exactly, and it's giving me weird results. It seems to be about 5x faster, than my regular method.


Hi Paul, here's a slightly more wordy description "off the top of my head":

For each ray initialise a float array called say "dists" of size maxiter entries each to say 1e200 and set "binary search" count to zero, set "step dstance" to say 1e200 and set current position on the ray then perform the following loop until current position is too large or solid is found

copy "step distance" to last step distance
calculate the values for the current position on the ray
Iterate the fractal formula (==iteration1) store iteration count as i1
if hit max iter
  if last step distance==1e200
    set "solid found"
    set found position=current position
  else
    set "binary search" count to 1
    set step distance = 0.5*last step distance
    set current position = current position - step distance
  endif
else
  calculate s1 = smooth iteration value for iteration1
  cacluate values for current position + 1e-10
  Iterate the fractal formula (==iteration2)
  if hit max iter
    if last step distance==1e200
      set "solid found"
      set found position = current position+1e-10
    else
       set "binary search" count to 1
       set step distance = 0.5*last step distance
       set current position = current position+1e-10 - step distance
    endif
  else
    calculate s2 = smooth iteration value for iteration2
    calculate v = 1.0/(1.0+1e10*abs(s1-s2))
    if v<minimum approach
       step distance = 0.5*last step distance
       current position = current position - step distance
       binary search = 1
    else if not binary search
      if dists[i1]<v
         v = dists[i1]
      else
         dists[i1] = v
      endif
      if dists[i1+1]>v
          dists[i1+1] = v
      endif
      step distance = v/(2.5*user detail parameter)
      set current position = current position + step distance
    else
       if binary search count>=max binary depth
          set solid found
          found position = current position
       else
          step distance = 0.5*last step distance
          if v<minimum approach
             current position = current position - step distance
          else
             current position = current position + step distance
          endif
       endif
    endif
  endif
endif

Edit: I just rechecked the original here: http://www.fractalforums.com/3d-fractal-generation/true-3d-mandlebrot-type-fractal/msg7812/#msg7812 and I think that's actually better smiley

Paul - are you sure you 1. calculated the smooth iteration values correctly ? and 2. used abs(s1-s0) in the DE calculation not just (s1-s0) ?


Edit2: OK, just re-read the original again - there's an error, if the first iteration does not reach max iter but the second does then you need to check to see if it's the first point on the ray (by checking last step distance for instance) and if so then set the point as "found" else if it's not the first point then you *do* need to institute the binary search rather than as I originally wrote it where it's just taken as being the "found" point anyway.
« Last Edit: September 26, 2009, 01:29:02 AM by David Makin » Logged

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lycium
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« Reply #239 on: September 26, 2009, 11:41:07 AM »

here's an unfinished render of those generalised julia sets:



i need to get my cpu cooling sorted out before i do any serious rendering with this computer Sceptical
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