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Author Topic: 3D Koch cube (escape time) + formula  (Read 9001 times)
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Tglad
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« Reply #15 on: May 02, 2011, 09:26:18 AM »

Yes, it is discussed a bit here: http://www.fractalforums.com/new-theories-and-research/categorising-fractals/msg22585/#msg22585
It's an example of a class of fractal of which there are so few examples of that there was no obvious name, so I called them shells. I'd like to build one out of card, but it would be an arduous job!


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visual.bermarte
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« Reply #16 on: May 02, 2011, 11:29:06 AM »

http://alt-fractals.blogspot.com/2011/04/impossible-snowflake.html
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Tglad
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« Reply #17 on: May 02, 2011, 12:01:14 PM »

And an alternative: http://www.fractalforums.com/ifs-iterated-function-systems/fun-with-koch-fractals/msg2630/#msg2630
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David Makin
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« Reply #18 on: May 02, 2011, 01:31:39 PM »

If you're desperate for a Koch (sorry couldn't resist) using the escape-time method and have Ultra Fractal (or ChaosPro I think) then you should be able to get one starting from one of the IFS parameter files here (2D or 3D):

http://ultrafractalwiki.fractalforums.com/Category:David_Makin

If doing 3D it might be best to reset the formula to defaults as a starting point - also the "Monument" is a good basic example of how to create Sierpinski architectures wink

Of course if using ChaosPro then you should import all the mmf*.ufm and mmf*.ucl files from the UF database before loading any of the above UPRs.
« Last Edit: May 02, 2011, 01:33:41 PM by David Makin » Logged

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DarkBeam
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« Reply #19 on: May 02, 2011, 06:37:23 PM »

Desperate for a Koch??? fiery rolling on floor laughing

Thanks for all the replies, I already knew that there is an huge number of possibilities, and I already have seen those you posted and others but I liked the most the Squarry Koch and the pyramid. cheesy

David can you share the exact 3D transform you used (edventually with a drawing)? It may come very handy Azn (but if it is made of more than 10 matrix don't care cheesy )
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DarkBeam
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« Reply #20 on: May 02, 2011, 06:57:28 PM »

Here is the render Knighty requested.

I know that is very good looking, but ... Not as good as it can look at a 1st sight

I used an HQ for the render, and it hides almost perfectly the noise (but there is a bit of it still...)

There are some unsatisfying strange flying things, but the "substance" is convincing

I modified a bit the original formula, adding an abs(z) in the end, and it seems to work better. Azn

Too bad, z offsets are not well accepted.

And still rotations don't work, I will enable them when the non-rotated fractal will look perfect! cheesy


* ryuko.jpg (251.95 KB, 700x950 - viewed 229 times.)
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DarkBeam
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« Reply #21 on: May 04, 2011, 08:15:16 PM »

I have ported this algorithm on MB, the result is cute but the noise is annoying. fiery

  if abs(x)>1 || abs(y)>1
  x = abs(x)
  y = abs(y)
  z = abs(z)
      x=abs(x);y=abs(y);z=abs(z);
      if(x-y<0)
      x1=y;y=x;x=x1;
      endif
      if(x-z<0)
      x1=z;z=x;x=x1;
      endif
      if(y-z<0)
      y1=z;z=y;y=y1;
      endif
  if (x-xlim)>y
   x = xsub1 - x
   y = yzsub1 -y
   z = yzsub1 -z
   x,y,z *= scale1
   else
   x = (xsub2 - x)*scale2
   y = (yzsub2 -y)*scale2
   z = (yzsub2 -z)*scale2
   endif
  endif

Scale1=Scale2 does not plot, so the only way is to set em differently

The cubes are not perfectly displaced, the formula is still approximated undecided

Params used

.Double Scale 1 = 4
.Double Scale 2 = 3
.Double x limit = .75
.Double dx1 = 1.25
.Double dyz1 = 0
.Double dx2 = 2
.Double dyz2 = 1.5

I am attaching the formula too, that gives nice results but is still noisy sad


* kochcub.jpg (67.95 KB, 588x623 - viewed 213 times.)
* sqkoch.m3f (1.41 KB - downloaded 120 times.)
« Last Edit: May 04, 2011, 08:17:41 PM by DarkBeam » Logged

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knighty
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« Reply #22 on: May 04, 2011, 11:26:37 PM »

Nice indeed. But this is not squarry Koch   tease .
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DarkBeam
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« Reply #23 on: May 04, 2011, 11:33:56 PM »

Nice indeed. But this is not squarry Koch   tease .
The wrong part is when I do y z second folding unconditionally, plus wrong values, what looks good in 2d may be horrible in 3d. More time needed, sir cheesy
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DarkBeam
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« Reply #24 on: May 05, 2011, 12:24:24 PM »

In fact... cheesy

Now it is okay, but the DE is a trouble. The renders are done with min iters = 8... undecided

  if abs(x)>clim || abs(y)>clim || abs(z)>clim
  x = abs(x)
  y = abs(y)
  z = abs(z)
      x=abs(x);y=abs(y);z=abs(z);
      if(x-y<0)
      x1=y;y=x;x=x1;
      endif
      if(x-z<0)
      x1=z;z=x;x=x1;
      endif
      if(y-z<0)
      y1=z;z=y;y=y1;
      endif
  if (x-xlim)>y
   x = xsub1 - x
   y = yzsub1 -y
   z = yzsub1 -z
   x,y,z *= scale1
   else
   x = (xsub2 - x)*scale2
   if y>yzlim
   y = (yzsub2 -y)*scale2
   endif
   if y>yzlim
   z = (yzsub2 -z)*scale2
   endif
   endif
  endif

correct settings are;

.Double Scale 1 = 3
.Double Scale 2 = 3
.Double x limit = .6666666667
.Double dx1 = 1.33333333
.Double dyz1 = 0
.Double yz limit = .333333
.Double dx2 = .6666666667
.Double dyz2 = .6666666667
.Double Carving limit = 1

* sqkoch.m3f (1.72 KB - downloaded 113 times.)

* kochcub.jpg (97.06 KB, 439x708 - viewed 217 times.)
« Last Edit: May 05, 2011, 12:25:56 PM by DarkBeam » Logged

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visual.bermarte
Strange Attractor
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Posts: 289


« Reply #25 on: May 09, 2011, 11:08:18 AM »

by chance i have found this amazing video showing a sqkoch
<a href="http://www.youtube.com/v/SbSo7onX9qI&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/SbSo7onX9qI&rel=1&fs=1&hd=1</a>
« Last Edit: May 09, 2011, 12:16:15 PM by visual » Logged
DarkBeam
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The spaghetti formula coder


« Reply #26 on: May 09, 2011, 01:16:06 PM »

FANTASTIC grin grin grin

I have done it, now it is continuous, it looks just like in your video (just without the sparkles evil ) anyway I didn't find the correct address for implementing the rotation angry fiery fiery

Now I will upload the code, this is the "pure formula" (escape time...) ideas on how to add more goodies? grin

Cubic Koch
  ; basic cubic fold (from Menger3 formula)
  x = abs(x)*scale
  y = abs(y)*scale
  z = abs(z)*scale
  if y>x
  t=x
  x=y
  y=t
  endif
  if z>x
  t=x
  x=z
  z=t
  endif
  if z>y
  t=y
  y=z
  z=t
  endif
  ; basic vars
  a=scale-1, b=scale+1, c=x-a, d=x-b
  ; Now, draw the cube WITHOUT making discontinuites in the spatial vars
  ; bring what falls "out of the small cube zone" in the interval (-1;1) (next iter will take care)
  ; z must be folded to get a homogen look (use zfix=1 for a normal koch cube)
  z=zfix-abs(zfix-z)
  if (c<y)
   ; out of the cube ... normalize
   x=c
   y=a-y
  elseif (d>y)
   ; point falls just over the small cube
   x=d
  else
   ; vertical faces of small cube (swap)
   x=y
   y=d
  endif
----------------


* kochcub illu.gif (3.35 KB, 339x185 - viewed 1012 times.)
« Last Edit: May 09, 2011, 01:47:57 PM by DarkBeam » Logged

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DarkBeam
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Posts: 1666


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« Reply #27 on: May 09, 2011, 01:37:45 PM »

Okay, the test parameter. I enabled very high quality (slow render), too bad the structure is hidden by some annoying artifacts in normal quality. sad

Mandelbulb3Dv16{
O.....S....O/...w....2A..............1.......s1E................................
................................OaNaNaNadz1........0./..................y.2.....
................/MU0A....6kHN...i/....E2.....QzIXLua2PrD...........c./...w1.D8Qx
w.EnAnQD1E../2.swsc1au1xz0r2VJpErBuD..IpM1t49x9..................y1...sD...../..
.wHnAngD2Rw3Oc.cazXAWreAEZc2zSWyooeAVOyjTcFzUvMS3t97C1JzzzzvzUNehUisqclj.Zh4j8Hc
aznAWreAEZc2zconlUV0UOyD......o90.....................sD..kz0...................
..............................MRS4.4qtN.kObb/UoRS4.srtN.sVbb/.FSS4..............
.....................wzzz1.U..6.P....M4...EB....W....61....F....8/...I1....UJl22
...U.iVFwxDE./ozPM2Tzz7lz16.mc..zXCc.El18XGQeGyDjvIRhrVAkz1............28.kFrA0.
FWb96aAIVzvh1se7Umvxz0........../6U0.wzzz1................................E.0c..
zzzz.................................2U.8.kzzzD.................................
/6U0.wzzz1...................................2CcN/UvNP6.eeWCNq0.yRii.EJJUk1f..XR
S1.mx3CcN/UvNP6.QsLsUa3.ibhV..bTV1OK.sSq40.ly3CcN/UvNP6.MwLsUa3.ibhV.kqTV1OK.sSq
40.kz3CcN/UvNP6...EsUa3.eeWCNq0.IJ36wk8.wyLsUa3.................................
E.E..2....E.....I....6....kOjB4OTBKRWJ4.7NoI............................4MU/4MU/
4M.................0./........zD...................0./..........................
................................................................................
........................}
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Tglad
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« Reply #28 on: May 09, 2011, 02:22:10 PM »

Excellent video, incidentally the sqkoch is a perfect example of a Tree-shell (https://3508742642023015005-a-1802744773732722657-s-sites.googlegroups.com/site/simplextable/what-is-the-simplex-table/classesOfFractals%282%29.jpg).
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knighty
Fractal Bachius
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Posts: 570


« Reply #29 on: May 13, 2011, 09:32:06 PM »

Ok! what about these two ones? grin
It's a mix between KIFS and msltoes' approache. The DE is not perfect: there are still some discontinuities but it's good enougth. Unfortunately those discontinuities are more severe if one changes the scale, offset or apply rotation. That may mean that hybrids would give some sand effect.

* koch20.zip (1.63 KB - downloaded 117 times.)
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