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Author Topic: Tglad's Mandelbox and using the delta DE methods for RIFS  (Read 12699 times)
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kram1032
Fractal Senior
******
Posts: 1863


« Reply #15 on: February 27, 2010, 07:27:52 PM »

WOW, great octahedral stuff cheesy
Looks nice'n smooth and stull fractal cheesy

And @ 2D-cellular automata:
Well, there are hundreds of 2D-cellular automata but I never saw one which is basically the direct extension of the 1D ones an maps time to the 3rd dimension....
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David Makin
Global Moderator
Fractal Senior
******
Posts: 2286



Makin' Magic Fractals
WWW
« Reply #16 on: March 02, 2010, 03:05:53 AM »

Hi all,

My wip3D5 formula for UF now includes "Simple Sierps" under the Mandelbulb/Juliabulb option (here due to the architecture of the formula).
The "Simple Sierps" options allow Location Restricted escape-time IFS based on Tglad's fractal type.

http://www.fractalgallery.co.uk/MMFwip3D.zip

Edit: Formula updated to include better colouring options. The main formula itself now features a "Lighting + Orbits" option which allows true 3D orbit trapping plus a "genetic" based colouuring option for Tglad's Mandelbox and for the "Simple Sierps" (ifs) method.

At the moment it's plain IFS with uniform scaling plus translation only but I'm working on a much more comprehensive formula incorporating most possible escape-time fractal types in one (as conditionally applied transforms).

Here are some examples using the "Simple Sierps" formula option:

A Menger Sponge:

Code:
QuickMengerSponge {
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}

Sierpinski Tetrahedron:

Code:
QuickSierpinskiTetrahedron {
; Copyright ę 2010 by David Makin.
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}

Sierpinski Octahedron featuring fogging:

Code:
QuickSierpinskiOctahedron {
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}

A Box Plant:

Code:
BoxPlant {
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}

Note that the Box Plant example shows how location restriction can be used to control the IFS - on transform #13 the "relative radius" is set to 2.75 to thin out the foliage. The "correct" value would be 1.5 but that produces a rather solid result smiley
« Last Edit: March 12, 2010, 10:06:36 PM by David Makin » Logged

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« Reply #17 on: March 02, 2010, 03:45:20 AM »

  David,

 Do you mind posting the math (can't read what you posted) for your Menger Sponge algorithm?

   I'm hoping (from what you've said) that it's more along the lines of Msltoe's radius formulas (similar to Tglads Mandlebox formulas) instead of the standard algorithms:  I've made 3d Cantor Dust, but no sponge.  sad

  Whatever the answer, thanks for the work you put into these various formulas. 
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« Reply #18 on: March 02, 2010, 04:03:03 AM »

 David,

 Do you mind posting the math (can't read what you posted) for your Menger Sponge algorithm?

   I'm hoping (from what you've said) that it's more along the lines of Msltoe's radius formulas (similar to Tglads Mandlebox formulas) instead of the standard algorithms:  I've made 3d Cantor Dust, but no sponge.  sad

  Whatever the answer, thanks for the work you put into these various formulas.  

It's actually very straightforward:
We define the 20 transforms for the sponge i.e. at the centres of the relevant cubes with a uniform scale of 3 each.
In the iterative loop we then check the distance of the current "z" locaton from the centre of each cube and choose the transform for which the centre is closest to z and then use the values from that transform for that iteration i.e.

loop:
   Find nearest centre/transform
   compute new z = transform scale*(z - transform centre)
   until |z|>bailout || numiter>maxiter

Actually I also add the normal "constant" value to each new z - but for the plain original sponge you need the Julia form with a constant of (0,0,0).

The distance estimate is simply the final z magnitude divided by the total scale which for the Menger is simply magnitude/(3^numiter).

Obviously it's pretty simple to adapt the above for more general IFS, though my implimentation sticks to uniform scaling and a translation per transform only. Adding non-uniform x/y/z scales is feasible I think but adding rotations is another matter.

You should note that for the Menger Sponge using Hart's method of interesecting the transformed viewing ray with a bounding sphere and/or cube is both faster and cleaner - though this method (with the analytical DE) does appear to be faster for the Sierpinski octahedron and tetrahedron, and of course allows the possibility of mixing affine and non-affine transforms which is not possible using Hart's method.


« Last Edit: March 02, 2010, 01:06:54 PM by David Makin » Logged

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« Reply #19 on: March 02, 2010, 08:05:15 AM »

  Thanks David, 

  I'm still having a problem, however.  I check my 7 knockoff points (center, 6 other cubes to remove), subtract their corresponding values and end up with this pseudo-Sierpinski octahedron instead of a Menger sponge:



  Matt
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« Reply #20 on: March 02, 2010, 01:04:53 PM »

 Thanks David,  

  I'm still having a problem, however.  I check my 7 knockoff points (center, 6 other cubes to remove), subtract their corresponding values and end up with this pseudo-Sierpinski octahedron instead of a Menger sponge:

  Matt

No - use the other 20 cubes, not the 7 empty ones - as you show using the 7 empty ones can give a Sierpinski Octahedron with a copy of itself in the centre (and in the centre of every sub-octahedron) smiley (I assume you used scales of 2 instead of 3 in that render ?)
« Last Edit: March 02, 2010, 01:08:32 PM by David Makin » Logged

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« Reply #21 on: March 02, 2010, 11:59:09 PM »

  Doyyyy <-- wish I could include a bouncing noise in the spelling of that word

  Thanks!  I just dropped in to see is you had answered.  I'll try that out after dinner.  Sheesh, and I was wondering where you got the number 20 from.  Hilarious.  cheesy

  Scale was 2, as you said.  Just checked it.  Bailout of 2, and simple bail check value of |x| + |y| + |z| (crisps it up a bit, instead of the rounded images we get with x^2+y^2+z^2), although it may be better to do a more complex check.



  David-  I end up with a Sponge in the center of my sponge: a Beavis and Butthead tattoo scenario.  Going to check my formula.
« Last Edit: March 03, 2010, 01:32:08 AM by M Benesi » Logged

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« Reply #22 on: March 03, 2010, 12:41:38 AM »

Dave,
Your applications of MMFWip3D are really cool! Great stuff.
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« Reply #23 on: March 03, 2010, 02:08:33 AM »

  David-  I end up with a Sponge in the center of my sponge: a Beavis and Butthead tattoo scenario.  Going to check my formula.

I'm guessing you've got 21 transforms instead of 20 i.e. you've left in the central cube smiley
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« Reply #24 on: March 03, 2010, 02:10:00 AM »

Dave,
Your applications of MMFWip3D are really cool! Great stuff.

Thanks Ron. I wish I had more spare time - my class-based version is not progressing very quickly sad
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« Reply #25 on: March 03, 2010, 08:42:36 PM »

 David-  I end up with a Sponge in the center of my sponge: a Beavis and Butthead tattoo scenario.  Going to check my formula.

I'm guessing you've got 21 transforms instead of 20 i.e. you've left in the central cube smiley

  It's 20 transforms (checked it: no central checkpoint (0,0,0), 20 transforms).  I could set it up to remove the central cube (if the pixel values are within the central cube, set my bail comparison variable to max_bailout+1) but that seems like cheating (it isn't, but if you got it with the 20 transforms, I should too).  Haven't found a nice bail point either.

  It's a whole recursive set within the set, within the set, within the set, within the set (which technically makes it something other than a Menger Sponge)...

  Doyyyy  <bouncing sound effect added> :  in mid message, I decided to check my initial radius check, which was set too low.  Incidentally, if you decide you want an infinitely recursive Menger Variant, set your initial radius checkpoint low.  

  If you haven't done it yet, setting bailout up this way (instead of magnitude bailout check) gives you a much crisper sponge:
if  ( |sx|>|sy| && |sx|>|sz| )     // sx, sy, and sz values are the names of my x, y, and z post-calculation values
   {   bail=|sx|;}                      // I check to see which has the highest absolute value, and set bail on that
else if (|sy|>|sz|)                    // if I haven't hit my iteration limit
   {   bail= |sy|;  }
else
   {   bail= |sz|;  }                 //  the whole concept is: if one of the values is outside of the sponge, bail out man!

  with your code:  until bail>bailout  instead of  until |z| >bailout

  With a sponge of "pseudo-volume" of 3^3   (3 is side length), I set bail check variable to 1.5 (side length/2) for a perfect Menger sponge:


  <-- and I was all like "I M G  !!!! /I M G"
« Last Edit: March 03, 2010, 09:08:26 PM by M Benesi » Logged

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« Reply #26 on: March 03, 2010, 08:53:01 PM »

  David-  I end up with a Sponge in the center of my sponge: a Beavis and Butthead tattoo scenario.  Going to check my formula.

I'm guessing you've got 21 transforms instead of 20 i.e. you've left in the central cube smiley

  It's 20 transforms (checked it: no central checkpoint (0,0,0), 20 transforms).  I could set it up to remove the central cube (if the pixel values are within the central cube, set my bail comparison variable to max_bailout+1) but that seems like cheating (it isn't, but if you got it with the 20 transforms, I should too).  Haven't found a nice bail point either.

  It's a whole recursive set within the set, within the set, within the set, within the set (which technically makes it something other than a Menger Sponge)...

  Doyyyy  <bouncing sound effect added> :  in mid message, I decided to check my initial radius check, which was set too low.  Incidentally, if you decide you want an infinitely recursive Menger Variant, set your initial radius checkpoint low. 

  If you haven't done it yet, setting bailout up this way (instead of magnitude bailout check) gives you a much crisper sponge:
if  ( |sx|>|sy| && |sx|>|sz| ) 
   {   bail=|sx|;}
else if (|sy|>|sz|)
   {   bail= |sy|;  }
else
   {   bail= |sz|;  }
  <-- and I was all like "I M G!"

Since I'm using distance estimation I'm not sure if using bailout to a cube would be of any help - I do have that option in my "3D IFS" formula which uses Hart's method - that's actually faster for rendering the sponge anyway.
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« Reply #27 on: March 03, 2010, 09:24:22 PM »

  I've never implemented DE, nor do I know what "Hart's method" is... suppose I should find it somewhere.

  ChaosPro does use a built in bisection algorithm, which seems to do a nice job, although some form of DE might be nice. 

  Do you get the crisp cubes with the DE method or are they the slightly "bubbly" looking cubes?
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« Reply #28 on: March 04, 2010, 02:52:27 AM »

  I've never implemented DE, nor do I know what "Hart's method" is... suppose I should find it somewhere.

  ChaosPro does use a built in bisection algorithm, which seems to do a nice job, although some form of DE might be nice. 

  Do you get the crisp cubes with the DE method or are they the slightly "bubbly" looking cubes?

You get crisp renders at smaller DE thresholds - here's a render with threshold 1e-3:



That render took 1 min 3 secs on this heap-o-junk, equivalent to around 21secs on a 2GHz core2duo.
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« Reply #29 on: March 06, 2010, 02:03:53 AM »

  That DE version looks plenty 'crisp' (no different from a similar 6 iteration one I did to compare).  The time to calculate appears to be pretty similar (accounting for our different cpus: I'm using a 2 gigahertz core 2 duo).

  Depending on what settings I use it either takes (exactly what you said according to ChaosPro's internal timer.. weird) 21 seconds for normal background detection, down to ~11.312 seconds for extremely soft background detection (no clipping occurs for the extremely soft setting, so it can apparently be used for the Menger Sponge). 

   Anyways, thanks for helping me with the formula.  Whenever I find a good freeware compiler I might ask for help with DE, unless I figure it out simply by reading your older posts. 
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