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Author Topic: Mandelbulber v2 - 2.03  (Read 4364 times)
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DarkBeam
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Fragments of the fractal -like the tip of it


« Reply #15 on: March 02, 2015, 06:11:17 PM »

Code:
void BuffaloIteration(CVector3 &z)
{
     double x2 = z.x * z.x;
     double y2 = z.y * z.y;
     double z2 = z.z * z.z;
     double temp = 1.0 - z2 / (x2 + y2);
     double newx = (x2 - y2) * temp;
     double newy = 2.0 * z.x * z.y * temp;
     double newz = -2.0 * z.z * sqrt(x2 + y2);
     z.x = fabs(newx);
     z.y = newy;
     z.z = fabs(newz);
}

I am experimenting this more flexible formula in MB3D with interesting results. smiley Where j is an user defined integer value 0 to 63. (this means this formula has 64 variants!!! afro )
In short words, a flexible combination of Buffalo, Burning Ship, normal and a sort of "folded C addition" (variant just invented wink but promising)
Of course the code above is untested (a pseudocode) embarrass

*deleted see pages -> -> *

If I understood right some youhn formulas don't even add constants to some axis? This would further enlarge the number of possible variants... cheesy

Test imagery



« Last Edit: March 06, 2015, 06:57:55 PM by DarkBeam » Logged

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youhn
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Posts: 696


Shapes only exists in our heads.


« Reply #16 on: March 02, 2015, 07:18:58 PM »

Ah, what a beautiful mess you made of it.  grin Let's dive in.

First to clear up some confusion. The escape time formulas in Mandelbulber are actually only the main part, without the adding-c piece (because it's the same for about all formulas). Stripped (made simple) code looks like:

Code:
switch (fractal->formula)
{
case mandelbulb:
{
bulbAux[sequence].r = r;
MandelbulbIteration(z, fractal, bulbAux[sequence]);
break;
}
                }
//addition of constant
switch(fractal->formula)
{
case menger_sponge:
case kaleidoscopicIFS:
case aexion:
{
break;
}
default:
{
if(in.common.juliaMode)
{
z += in.common.juliaC;
}
else
{
z += c * in.common.constantMultiplier;
}
break;
}
}

Are those images this power 2?? Looks a bit like a higher power bulb. So if I understand you're code, then jj 0 and 1 are what I already have. Then jj 2 adds c before folding (this is new for me) and else (for every jj up to 63 ... ?) some rather strange magic happens (also new for me). That second image sure looks nice, so I'll give it a try.
« Last Edit: March 02, 2015, 07:29:57 PM by youhn » Logged
DarkBeam
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Fragments of the fractal -like the tip of it


« Reply #17 on: March 02, 2015, 08:02:20 PM »

Well lol, j contains packed the variants of the formula wink

to unpack use binary numbers j = 01 11 00
So, j and 3 isolates last 2 bits smiley So j and 3 = 00, the variant used for X will be the first
Shr j,2 rotates bits... j = 01 11, and new j = 11, the variant used for Y will be the 4th
Shr j,2 rotates bits... j = 01, and new j = 01, the variant used for Z will be the 2nd

Clear I hope grin grin

Oh thos images are j-sets smiley
« Last Edit: March 02, 2015, 08:04:21 PM by DarkBeam » Logged

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DarkBeam
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Fragments of the fractal -like the tip of it


« Reply #18 on: March 02, 2015, 08:16:20 PM »

It will be not easy to replicate the results in mandelbulber if the c addition is done afterwards...  huh? dunno...
In my formulas there is no c addition afterwards, so the buffalo variant is out of reach wink
« Last Edit: March 02, 2015, 08:22:17 PM by DarkBeam » Logged

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youhn
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« Reply #19 on: March 02, 2015, 08:32:19 PM »

I think you'r jj == 1 condition is a buffalo. Number 7 in the numbering from https://code.google.com/p/mandelbulber2/wiki/BuffaloFractals

In Mandelbulber the conditions should be in both the main formula and the adding-c part, should be doable.
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DarkBeam
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Fragments of the fractal -like the tip of it


« Reply #20 on: March 02, 2015, 09:13:45 PM »

Also I can tell you, a more good looking option is to not change the sign of z;

void BuffaloIteration(CVector3 &z)
{
     double x2 = z.x * z.x;
     double y2 = z.y * z.y;
     double z2 = z.z * z.z;
     double temp = 1.0 - z2 / (x2 + y2);
     double newx = (x2 - y2) * temp;
     double newy = 2.0 * z.x * z.y * temp;
     double newz = +2.0 * z.z * sqrt(x2 + y2);
     
     z.x = AddCCondit(newx, c.x, j); shr (j,2);
     z.y = AddCCondit(newy, c.y, j); shr (j,2);
     z.z = AddCCondit(newz, c.z, j);
}

smiley More images coming
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DarkBeam
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Fragments of the fractal -like the tip of it


« Reply #21 on: March 02, 2015, 09:20:39 PM »



A variation with positive z, looks good wink, while the negative version is awful sad
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youhn
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« Reply #22 on: March 02, 2015, 09:25:51 PM »

Try slicing them through either the XY or XZ plane to see what 2D fractals are hidden.  nerd
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knighty
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« Reply #23 on: March 02, 2015, 09:29:00 PM »

 Repeating Zooming Self-Silimilar Thumb Up, by Craig
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cKleinhuis
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formerly known as 'Trifox'


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« Reply #24 on: March 02, 2015, 09:30:38 PM »

@darkbeam
isnt this not just taking the absolute value of result of any combination of the 3 axis x/y/z ?

i need to try it out on shadertoy wink
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DarkBeam
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Fractal Senior
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Posts: 2512


Fragments of the fractal -like the tip of it


« Reply #25 on: March 02, 2015, 10:24:23 PM »

@darkbeam
isnt this not just taking the absolute value of result of any combination of the 3 axis x/y/z ?

i need to try it out on shadertoy wink
Eh, no smiley read more in detail! smiley cheers Knighty!

And you(hn) must wait for xsections ... wink
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DarkBeam
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Fragments of the fractal -like the tip of it


« Reply #26 on: March 03, 2015, 04:49:21 PM »

... okay wink



You can see that abs(x+cx) doesn't give the Buffalo fractal, but Celtic Mandelbrot; it's the image in the top.

EDIT nooo... cheesy the correct image is that on the bottom! But I don't remember the right number to put cheesy

« Last Edit: March 03, 2015, 04:54:29 PM by DarkBeam » Logged

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DarkBeam
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Fragments of the fractal -like the tip of it


« Reply #27 on: March 03, 2015, 06:12:30 PM »

The confusion came from the fact that my formula has a different setting, that makes tricky to find variations;
I really wanted to make Buffalo variation the default one, so I assigned the number zero to it! But I just forgot fiery Oh well
In my opinion the very best buffalo is the one that multiplies z and y by a negative number (not positive)
It's not eassy to tune perfectly a variation because many variations are available snore
By the way the only one that is a Buffalo in xy and xz section is something like

{
     double x2 = z.x * z.x;
     double y2 = z.y * z.y;
     double z2 = z.z * z.z;
     double temp = 1.0 - z2 / (x2 + y2);
     double newx = (x2 - y2) * temp;
     double newy = -2.0 * z.x * z.y * temp;
     double newz = -2.0 * z.z * sqrt(x2 + y2);
    
     z.x = AddCCondit(newx, c.x, j); shr (j,2);
     z.y = AddCCondit(newy, c.y, j); shr (j,2);
     z.z = AddCCondit(newz, c.z, j);
}

When jj = 010101b = 21d using my convention

This is not true for just any variation, some look great only when all variables are positive alien
(edit!!! Lied - this particular variant doesn't care of signs sad - all good)

The pretty pic (just for Christian cheesy ) ;



MB3D parameter

Mandelbulb3Dv18{
g....EQ0...l7...w....2....UVDgdmf5a/.fu5IBKCVL8E7uiCIUxpqz1kOUC6fnLxzI8PXeAfiizD
........................................kz1........A./..................y.2...wD
...Uz6....E11.../M.0/......f0...W/....E3......rlZbMAujoD/......./KX.1dkpXm1.OaNa
y.EnAnYD12../.EL9lhTo6Iqzq3KcOUSpUwDdLc0Da3ZYz1...........U0.....y1...sD...../..
.z1...sD4OvPjHwy/xfzA/eyCuKFz24laqdQNOYjlTPN8Z2XvwP0qHUwYplBz03kFAEBjJoDbj/mmVqO
.xXP6VXvBtsCzcNsRZkzu5oDU.....2vI.............sD.6....sD..G.0...................
.............oAnAt1...sD....z...........................................w....k1.
.....Ksulz1.......kz.QHgT1.U..6......U5...EQ....m....c3...U.....L....I1.....SJ52
wI0U.qFG90kb2zz3....j.....6.pc..zXCc..kvrEtMc7xD6ocyFE0ujz1..........2.28.kFrA0.
.Ub96aAIVz9.1se7Umvxz0........../EU0.wzzz1...........s/...................E.2c..
zzzz.............0...................2./8.kzzzD............8....................
/EU0.wzzz1...................................chQZ.EB85YvqPGeFv0.pcQEbjVA6hB7.IXm
/tiXv2YLy0EB85YveroSXkB.pcQESTJNYjFa.IXm/timodhQZ.EB85Yv/PbqmJ0.pcQEib7TO9L7.IXm
/tSWydhQZ.EB85Yv..EsUa3feeWCNqGQIJ36wk8EwyLsUa3f................................
E....2..F2E.....I....M....EIp34NnEYM..pPrJaQ.sqNgJqQ........................0...
...................wz..........k..........A...................zD................
................................................................................
........................}
{Titel: true buffalo}

(ps I cheated with some effect to show those blue bands cheesy )
« Last Edit: March 03, 2015, 07:30:56 PM by DarkBeam » Logged

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mclarekin
Fractal Senior
******
Posts: 1739



« Reply #28 on: March 04, 2015, 08:51:32 AM »

Cool post chaps. I particularly like DarkBeams strategy to deal with variants, (opposed to having a unmanageable clutter of variant fractal files  sad)
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youhn
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Posts: 696


Shapes only exists in our heads.


« Reply #29 on: March 04, 2015, 05:25:35 PM »

I think some checkboxes are more transparant and give a better overview, when given together with a short explanation what the option do:



Still have to add the magic inside Luca's AddCCondit routine to the Buffalo fractal in Mandelbulber.
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