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Author Topic: Bulb Mutation Games  (Read 504 times)
Description: A thread to collect some (basic) mutations of the 3D Mandelbulb
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gannjondal
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Posts: 17


« on: March 04, 2017, 12:14:41 AM »

It was already a few weeks ago that I had seen some works of Sabine on her dA account in which she played with the common Mandelbulb formulas in Fragmentarium (she called it "mandelbulb-mistreatment").
That remembered me to an old bad habit of mine where I tried such mutation games for the mandelbrot set (or other formulas) in 2D.
Finally I have started this old game again for the common 3D Mandelbulb in M3D (using the JIT feature).

I also remembered that some time ago I tried to search for mutations here in the FF. There have been several threads that could be placed into such a category.
However, I did not see a thread asking explicitely "Hey, lets play, and try to mutate the formula xyz".
Of course I don't know the complete forums - so please do not hesitate to bang my had to the next wall, and to tell me that I'm too stupid to search ;-)

And now I have read DarkBeam's recent thread at http://www.fractalforums.com/the-3d-mandelbulb/mixed-two-stage-bulbs/ .
That was the last trigger for me to start this thread just now (as I'm not the only person who is playing this game).

I know that I have not many posts in the forums yet, so that I'm probably not the perfect person to start such a thread :-)

But anyway, I want to try it. --
Of course I want to present some of my results ;-)
But also I want to invite you to this game.

This is what I'm thinking about.
Any ideas, changes... would be appreciated.

  • Topic:  Let's mutate the classic Mandelbulb formula (to give at least a bit of rule)
  • No restrictions regarding the used program
  • Mathematical useless changes are allowed - No, they are desired
  • The formula changes may be wired - but the resulting pictures should not look like a cloud of pixels :-)
  • Feel free to add some hybrids as examples to show how the changed formula can be used

The background of the last point is:
It turned out to be quite difficult to change especially the Mandelbrot set (but also the 3D Mandelbulb to a certain extend) in a useful way:
The formula is so simple that every change runs the risk to destroy the picture completely.
Using hybrids (especially unchanged Mandelbulbs) is one way to reduce the dose of mutations, so that something interesting may come out even for a weird change (there are other ways; however that would be another thread ;-)).

Ok. Enough of jabber.

At the very beginning I want to start with 3 -quite simple- examples of changes - see below replies ....
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gannjondal
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Posts: 17


« Reply #1 on: March 04, 2017, 12:37:07 AM »

Sample 1

Program:   MB3D
My name of the m3f formula:   JIT_gnj_RealPower_m06b.m3f (attached)

Sample animation:
(Mandelbulb3D .m3a file is here)


--> Changed params:
       In one half of the animation only MutationX/Y/Z (of course the mediation strength).
       In the other half also FacY, and FacZ (this simply adds FacY*z , respective FacZ*z while calculation of the individual components)

Parameter recommendation:
Start to change only MutationZ. For my feeling the result is the most interesting.

Still image:

MutationZ = 1; everything else matches the default values of the attached .m3f (as in below pictures):

 
Formula / Mutation:
To show the structure of my CommonBulb formulas I want to provide a more complete listing of the formula:
Code:
    // calculate the radius 
       sq_r := x*x+y*y+z*z;
       r := sqrt(sq_r);
   
    // calculate the sperical angles
       phi := ArcSin(z/r) ;
       theta := -ArcTan2(x,y) ;
   
    // calculate the power for the spherical coordinates, and the related angles
       r_pow:= power(r, Power_);
       phi_pow := phi*Power_;
       theta_pow := theta*Power_;
   
    // Calculate sin and cos
       SinCos(theta_pow, sth, cth);
       SinCos(phi_pow, sph, cph);
   
    // Mutation
       x_tmp := x*x + FixSqrX;
       x_tmp := MutationX*z*y/x_tmp + FacX*x;
       
       y_tmp := y*y + FixSqrY;
       y_tmp := MutationY*x*z/y_tmp + FacY*y;
       
       z_tmp := z*z + FixSqrZ;
       z_tmp := MutationZ*y*x/z_tmp + FacZ*z;
       
    // Bring it together (normal bulb calculation)
       x := x_tmp + CommonBulbX*cph*cth*r_pow + cx;
       y := y_tmp + CommonBulbY*cph*sth*r_pow + cy;
       z := z_tmp - CommonBulbZ*sph*r_pow + cz;

* JIT_gnj_RealPower_m06b.m3f (2.6 KB - downloaded 61 times.)
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gannjondal
Forums Freshman
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Posts: 17


« Reply #2 on: March 04, 2017, 12:47:37 AM »

Sample 2

Program:   MB3D
My name of the m3f formula:    JIT_gnj_RealPower_m07a.m3f  (attached)

Sample animation:
(Mandelbulb3D .m3a file is here)


--> Changed params:
      Mainly MutationX/Y/Z , and FixTanTheta/Phi
      At one point also CommonBulbZ is changed (so far I see equivalent to the negative of the 'Z multiplier' in normal M3D bulb formulas; but I'm not sure) 
 
Still images:
MutationY = 0.5


MutationZ = 8


Formula / Mutation:
Code:
    // Mutation
       tan_th := sth/(cth + FixTanTheta);
       tan_ph := sph/(cph + FixTanPhi);
   
       x_tmp := -z*tan_th + y*tan_ph;   
       y_tmp := x*tan_th + z*tan_ph;
       z_tmp := y*tan_th - x*tan_ph;
       
    // Bring it together (normal bulb calculation)
       x := MutationX*x_tmp + CommonBulbX*cph*cth*r_pow + cx;
       y := MutationY*y_tmp + CommonBulbY*cph*sth*r_pow + cy;
       z := MutationZ*z_tmp - CommonBulbZ*sph*r_pow + cz;

* JIT_gnj_RealPower_m07a.m3f (2.39 KB - downloaded 62 times.)
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gannjondal
Forums Freshman
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Posts: 17


« Reply #3 on: March 04, 2017, 12:58:00 AM »

Sample 3

Program:   MB3D
My name of the m3f formula:   JIT_gnj_RealPower_m08a.m3f (attached)

Sample animation:
(Mandelbulb3D .m3a file is here)


--> Changed params:
       FacY/Z , CommonBulbY/Z

Still images:
CommonBulbY = 0; FacY=0; Power=3


FacX = 2; FacZ = 1; Power=3


Hybrid:
This picture was the reason to think about a post to FF :-)


-->  Params:
Mandelbulb3Dv18{
g....EN2...QL...w....2....EqTdlxhcMwzOaNaNaNaZ0EBohbmem0A.AIYkx1XU6PzqBdop6SzguD
................................XQ3iMQRYG.2........Y./fa/..............UF/2...wD
...Uz6....kC/1...Y.0/....2Ef5...0/....Ej.....EpKXLak6flD/Y........2b1dNaNw1....G
/JEnAnQD16../2k6pjY./F21.jmFMa5um2rDZVjwrIJHyy9...........k1.....y1...sD...../..
.z1...kDhNaNjiKtku1y3xHTXl9IzGuKgIECMUjDBlvGu2E8iw1myqESWOvxykNQF3YHC/pDcsJgD4qH
Ex90b4D4yQNoy2Hr58xmbsmDUoAnAvHzD/..Ej0.......sD/A....sD..G.....................
.............oAnAt1...sD....zw1...................................UNaNCEC....k1.
.....4iSoz1.......kz2xzzz1Uc.A/.j/...Y6...U8....u/4V1.2.UNkE....5/...kX0....SJz/
Fo3U.ydelyjeYFnzyOwmzrdbB06.kAmzzzzz..klrlkCx9zD6.cXcESLfz1...........k.mwzXWF1.
.sM93P58iz9.MmnWK2zwz8..........26W2.E26L...YblEeTM4.vUbrD1Vzntj.cCVcAxWwz1/UQXz
2pm3..UbvUoLct.k.SUBU4cB.y9.dT7CwddAz.UBXwzuRH9..w8pJs/mpz982RiGMQZtz...........
36GC/oH9T...luxL45Zrz0Enq1Rf./yD.Iakuq/mNz1...uBZ..O4NX7ZCFoTu2.fhYCocm7nueM.kJD
hYnmus6Ul/.M07n6ko2crI0.QdX8a2VJUSH7.6LI.NGvS/uBZ.UQE/Y7cS4crI0.Rhn8aI6QUSH7.Y4G
sMGSt/uBZ.EM//X7...crIGJzzFoTuIdyzngi8qdxzZX.4rU................................
E....6E.F2k.....I....U....EE0x4SHpqPjF5O4x4PY/........................k/..U..6..
..........UaNaNaNaNyz2h6PbjTeFxD..........2Y0LD8Qxckz........./Eel9RHW//qz1.....
...2.ttvbOwGrYwD................................................................
.....................2.....3....5....cIGIxpNidqLGJKMg/pPrJaQTp4As24.............
..............................zD...................wz.....................2.....
.............U.E................................................................
................................}
{Titel: structurissima}


Formula / Mutation:
Code:
// Bring it together (normal bulb calculation) - plus the mutation
   x := CommonBulbX*cph*cth*r_pow + FacX*x + cx;
   y := CommonBulbY*cph*sth*r_pow + FacY*y + cy;
   z := -CommonBulbZ*sph*r_pow + FacZ*z + cz;

* JIT_gnj_RealPower_m08a.m3f (2.08 KB - downloaded 59 times.)
« Last Edit: March 04, 2017, 01:51:18 AM by gannjondal » Logged
DarkBeam
Global Moderator
Fractal Senior
******
Posts: 2512


Fragments of the fractal -like the tip of it


« Reply #4 on: March 04, 2017, 11:42:08 AM »

Please can you try to help me smiley

Try this combination and see if it works; (formulas taken from http://www.fractalforums.com/index.php?topic=2062.0 )


* rtrr.png (8.74 KB, 619x225 - viewed 105 times.)
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No sweat, guardian of wisdom!
mclarekin
Fractal Senior
******
Posts: 1739



« Reply #5 on: March 05, 2017, 12:47:49 AM »

@ gannjondal I like that hybrid image above.

M3D  JIT is a wonderful tool!!! 

This image from Mandelbulber V2.10, is made from mixing a standard bulb with  Mbulb Bermarte and Mbulb Kali, and the fractal maths runs for just 4 iterations

Quote
# Mandelbulber settings file
# version 2.10
# only modified parameters
[main_parameters]
ambient_occlusion_enabled true;
camera 0 0 3;
camera_distance_to_target 3;
camera_rotation -90 -90 -90;
camera_top 0 1 3.749399456654643e-33;
DE_factor 0.1;
flight_last_to_render 0;
formula_1 65;
formula_2 94;
formula_3 92;
fractal_rotation 0 0 90;
hybrid_fractal_enable true;
image_height 800;
keyframe_last_to_render 0;
main_light_alpha 0;
main_light_beta 0;
mat1_is_defined true;
view_distance_max 9.582187544707839;
[fractal_1]
power 8;
[fractal_3]
beta_angle_offset 360.7;
transf_pwr_8 4;
transf_scaleA_1 3;
transf_scaleB_1 0;


* bulb aaa6 s12.jpg (242.02 KB, 644x672 - viewed 112 times.)
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gannjondal
Forums Freshman
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Posts: 17


« Reply #6 on: March 05, 2017, 03:29:23 PM »

@DarkBeam:
I have added a comment to your thread, http://www.fractalforums.com/the-3d-mandelbulb/mixed-two-stage-bulbs/ . I think the questions are related, but please correct me if needed.
If I should find a result of mixing different bulbs, I will post it.

@mclarekin:
Thank you; you provided me a reason to try the new Mandelbulber again smiley
Indeed that specific hybrid caused me to continue to mutate around  Yes !! .

I love the M3D features as well -also if it has enough weaknesses- and would wish that more people would use it.
Honestly in earlier times I used the Mandelbulber more often than today (sorry smiley), and was a bit sad that the development of the old OpenCL version had been stopped (although I understand the reasons). But so far I see there is still some hope...
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gannjondal
Forums Freshman
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Posts: 17


« Reply #7 on: March 14, 2017, 12:15:36 AM »

Simple Mutations of Cartesian Calculations (of a power 8 bulb)

Program:  MB3D

Notes:
All previous examples have based on trigonometric calculation of (negative sine) bulbs of an arbitrary power n.
In this reply I'm posting some variations of simple mutations of a cartesian calculation that was explained in  this response (I just turned sine to the more common negative sine variant by changing z -> -z).

One advantage is of course that it's MUCH faster than tigonometric calculations.
Another advantage is:  As more terms a calculation has as easier it is to make small changes that don't destroy the whole picture. - Although you can see that you still can destroy quite much.

A 'disadvantage' is:  It's not that trivial to add partial rotations for components, therefore the most useful changes are quite global.

Still image:


Attachments:
- BulbCartesianAndSimpleMutations - m3f (JIT) formulas, and a formula readme
- slices_readme.txt - Overview about the above pictures (01* - 07* is of course seen from left to right). Includes the MB3D parameters.

* BulbCartesianAndSimpleMutations.zip (8.59 KB - downloaded 61 times.)
* slices_readme.txt (11.33 KB - downloaded 59 times.)
« Last Edit: March 14, 2017, 01:25:35 AM by gannjondal » Logged
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