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Welcome to Fractal Forums > Fractal Software > 3D Fractal Generation > Mandelbulb 3d > A few formulas (For Luca... :D)
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Author Topic: A few formulas (For Luca... :D)  (Read 12771 times)
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M Benesi
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« Reply #45 on: November 01, 2015, 06:17:09 AM »
Quote from: mclarekin on November 01, 2015, 04:39:31 AM
Set up the Benesi_Transforms UI with a magFoward at the beginning with a magBack half way down and lots of transforms in between. Was interesting when I used the UI  to recreate T1 out of five transforms, as there was not much increase in render time.
  Cool.  The rotations don't use trig functions, since we use precalculated square roots and the like... and the z^2 pine tree is all algebra too.  Makes it fast. 

Quote from: mclarekin on November 01, 2015, 04:39:31 AM
And I must see if I can get the DE calc working ( generally outside my ability.)
  DE is pretty easy for this one. Keep a running derivative, multiply by the transforms scale.. if you use a non-vector scale!  To do the vector scale like you're doing, you're going to need to do some fancy footwork...


  T1 really is a good base to go from.. then throw another one in there every once in a while.  I'm liking t4 the most now, but might switch back to T2... should add that to the .frag.  Still learning the frag stuff...
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mclarekin
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« Reply #46 on: November 01, 2015, 11:23:23 AM »
I have been just having fun with the magTransforms on there own, but  attached is random examples  with Mbox, Mbulb and Menger_Sponge.

A bonus is using magForward & magBack  to orientate the fractal to vertical symmetry.

DE calcs are more than halving render times grin afro.

Well when making a basic scale transform I came across this fancy footwork problem. And  considered  Laplace & Lagrange but in the end decided on summing the components and dividing by three. grin

Cheers

* MboxMbulbMgr3.jpg (199.63 KB, 1500x388 - viewed 197 times.)
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M Benesi
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« Reply #47 on: November 01, 2015, 05:35:26 PM »
lol.. the one on the right looks quite amusing... although I am easily amused at times.  cheesy 
Quote from: mclarekin on November 01, 2015, 11:23:23 AM
Well when making a basic scale transform I came across this fancy footwork problem. And  considered  Laplace & Lagrange but in the end decided on summing the components and dividing by three. grin
I was thinking the length of z divided by three, tested it, didn't work... didn't do your thing.  nice that that works.  Can add it to other things...
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ericr
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« Reply #48 on: November 02, 2015, 10:10:48 PM »
Where are "magTransforms on there own, but  attached is random examples  with Mbox, Mbulb and Menger_Sponge." for mandelbulb3d

ericr

 
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mclarekin
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« Reply #49 on: November 04, 2015, 04:32:39 AM »
@ M.Benesi  summing  fabs(scale. x y & z) /3 will  work when scale.x, scale.y & scale.z are the  similar, I have yet to retest when they are dissimilar.

Added six variables   for  pow( ) in T5B. Have yet to test.

 I recoded all the transforms, learning from your code that I can do   z  = CVector3 ( maths   , maths  , maths   ); grin
Spent all of yesterday fixing the bugs I had then created, sometimes I wish I was born an android, it is that human factor that causes me problems.LOL

And  now I should retro-fit rotations. 


 So I currently  now have all these transforms/formulas working in Mandelbulber grin


 
Code:
void benesiMagForwardTransformOneTransform3D(const sTransformBenesiMagForwardTransformOne &benesiMagForwardTransformOne, CVector3 &z, int i);
void benesiMagBackTransformOneTransform3D(const sTransformBenesiMagBackTransformOne &benesiMagBackTransformOne, CVector3 &z, int i);

void benesiMagTransformOneTransform3D(const sTransformBenesiMagTransformOne &benesiMagTransformOne, CVector3 &z, int i, sExtendedAux &aux);
void benesiMagTransformOnePlusMinusTransform3D(const sTransformBenesiMagTransformOnePlusMinus &benesiMagTransformOnePlusMinus, CVector3 &z, int i, sExtendedAux &aux);
void benesiMagTransformTwoTransform3D(const sTransformBenesiMagTransformTwo &benesiMagTransformTwo, CVector3 &z, int i, sExtendedAux &aux);
void benesiMagTransformThreeTransform3D(const sTransformBenesiMagTransformThree &benesiMagTransformThree, CVector3 &z, int i, sExtendedAux &aux);
void benesiMagTransformFourTransform3D(const sTransformBenesiMagTransformFour &benesiMagTransformFour, CVector3 &z, int i, sExtendedAux &aux);
void benesiMagTransformFiveBTransform3D(const sTransformBenesiMagTransformFiveB &benesiMagTransformFiveB, CVector3 &z, int i, sExtendedAux &aux);

void benesiFastPwr2PineTreeTransform3D(const sTransformBenesiFastPwr2PineTree &benesiFastPwr2PineTree, CVector3 &z, CVector3 &c, int i, sExtendedAux &aux);
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M Benesi
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« Reply #50 on: November 04, 2015, 06:39:45 AM »
  Nice coloring...  Since this is the help thread....


  Update.  Having a bit of problems with the coding the assembly portions.  I probably did something silly.  Not sure about the jmps and conditionals, since I'm not used to assembly.

  Anyway, posting the code in this thread for Luca (or anyone who wants to debug it) to look at.  I'll hack at it more tomorrow. 

  I might be dividing in the wrong order.. (fdiv or fdivr???) or.. maybe I added a command after the jump command... haha.. I don't know.  Tired.
* BenesiSpheric.m3f (5.66 KB - downloaded 76 times.)
* BenesiUnSpheric.m3f (3.76 KB - downloaded 76 times.)
« Last Edit: November 04, 2015, 08:48:54 AM by M Benesi » Logged
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M Benesi
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« Reply #51 on: November 04, 2015, 07:45:50 AM »
Awesome... I'm adding the cube to sphere and sphere to cube to M3D.   
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DarkBeam
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« Reply #52 on: November 04, 2015, 11:55:17 AM »
Finally had time to look at your works! wink

1) The transforms look OK but the DEoption must be different. That should be the reason why the images look bad currently.
2) Some of your formulas are a mystery to me; why they look like a quaternion? (No visible fractal detail)
Why redo IQbulb?
Why IQpinetree looks like a tricorn? Probably sign mistake/flipped Cx and Cy?

Some work is needed. And transforms need a _ prefix before too. wink

PS Have you got a non-trigonometric expansion for IQ formula (even just for power 2)? Would be greatly appreciated!!! Azn
« Last Edit: November 04, 2015, 12:01:49 PM by DarkBeam » Logged
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DarkBeam
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Fragments of the fractal -like the tip of it
« Reply #53 on: November 04, 2015, 06:19:10 PM »
Here I simplified a bit spheric (less temporary stuff & grouped some multiplications) + I will rename it with a _ prefix, added proper DE option (works perfect) wink
The only way to see which is good (div or divr?) is to test it directly with ollydbg; put two numbers in the stack and see which works each time or you will pick the wrong one grin

Code:
[OPTIONS]
.Version = 2
.DEoption = -1
.Double Scale = 0.81649658092773
[CODE]
558BEC81EC300000005356578B75088B7E308BD8D9D0DD02D8C8DD55F8DD01D8
C8DD55F0DEF9D9E8D8D9DFE080E4417E04D9E8DEF1D9E8DEC1D9FADD5DE890DD
45F8DC45F0DD03D8C8DEF9D9E8D8D9DFE080E4417E04D9E8DEF1D9E8DEC1D9FA
DC4FF0D9C0DC4DE8DD5DE8DD5DF090DD03DC4DF0DD02DC4DE8DD01DC4DE8DD19
DD1ADD1BD9D08BC35F5E5B89EC5DC20800
[END]


Description:

Warps a cube to a sphere; transform made by M.Benesi, optimized by
Luca.

/ spheric  code
 rCyz= (z.y*z.y)/(z.z*z.z);
 rCxyz= (z.y*z.y+z.z*z.z)/(z.x*z.x);
if (rCyz<1.) {rCyz=sqrt(rCyz+1.);} else {rCyz=sqrt(1./rCyz+1.);}
if (rCxyz<1.) {rCxyz=sqrt(rCxyz+1.);} else {rCxyz=sqrt(1./rCxyz+1.);}

z.yz*=rCyz;  
z*=rCxyz/sr32;
[/code]
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M Benesi
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« Reply #54 on: November 05, 2015, 05:56:36 AM »
You're awesome Luca.  Thanks!

  I'm going to try to flip that code for the unSpheric option after I finish this sphere to tetrahedron transform I'm working on.  For the cool "squares" you do Transform 1 (not pine tree!), unspheric, pine tree, spheric, on whatever iteration you want the cubes to appear.

  I'm working on a sphere to tetrahedron transform... and will probably make a tetrahedron to sphere as well.  With those, we will be able to blend Sierpinski and a Menger, with other stuff... cheesy
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M Benesi
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« Reply #55 on: November 05, 2015, 07:58:07 AM »
Here is the "unSpherical" .m3f


  Do a pine tree or 2, T1, this, Pinetree x pixel, spherical, repeat...  for a few squarey sections.  cheesy

* BenesiLucaUnSpheric.m3f (4.08 KB - downloaded 82 times.)
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DarkBeam
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Fragments of the fractal -like the tip of it
« Reply #56 on: November 05, 2015, 08:27:46 AM »
 A Beer Cup
I am curious: difference between spheric/unspheric? wink edit! Got it just that the sqrt(...) becomes 1/sqrt(...) wink
Editedit: Nope... I will keep your version as mine fails! cheesy A form of allergy perhaps? sad
Going to update "my" formula file now!
Pls reply to my questions above too afro
« Last Edit: November 05, 2015, 10:32:26 AM by DarkBeam » Logged
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M Benesi
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« Reply #57 on: November 05, 2015, 11:03:55 AM »
Quote from: DarkBeam on November 04, 2015, 11:55:17 AM
Finally had time to look at your works! wink
I thought you were talking about Mclarekin.. sorry.  lol.. This thread is all over the place.  

Quote from: DarkBeam on November 04, 2015, 11:55:17 AM
1) The transforms look OK but the DEoption must be different. That should be the reason why the images look bad currently.
 Ok, I probably need a few pointers. wink  maybe I should re-read stuff that you've told me..but I get caught up in stuff and miss it.  Sooo....  I might not set the DEoption things correctly.

  I did make a DE version for Fragmentarium (just do scale of Transforms, then standard .5*log(r)*r/dr (dr*scale for the transform iterations, *power for the pine tree section, etc...).

Quote from: DarkBeam on November 04, 2015, 11:55:17 AM
2) Some of your formulas are a mystery to me; why they look like a quaternion? (No visible fractal detail)
 Ok.  The "no YZ" ones don't have the y and z pixel component added in, which is why they look a bit like a spun Mandy.  What I need to do is change them, so they have pixel multipliers in the formula.  Then all of the extra formulas, like pine treeX  (which is only x pixel!) and PineTree1noYZ (no y z... only x, but it HAS the transform with it.  You need only pine tree, without transform 1, for certain things like the following:

Code:
Mandelbulb3Dv18{
g.....S....O/...w....2....kFvS./.....980zxzzzr1EIqupJ0QfnwHS4trZ.ruAzAZrFKNa3U.E
................................OaNaNaNadz1........A./..................y.2...wD
...Uz6....k2..../MU0/.....ke....2/....E3.....QzIXLua2PrD/..........m/dkpXm1....U
z.....kD12../..........wz.................................U0.....y1...sD...../..
.z1...sDECayXi7lax1..........WjJy0vma8djv8jrnNkXyq9YXdzcPGgNzEEnhwuma8dj2oQ9jigd
GuHyKt9g9PeYyYmQF6ua2PqDU.....2J..............sD.6....sD..G.....................
.............oAnAt1...sD....zw1.........................................A....k1.
.....Ksulz1.......kz.wzzz1.U..6.P....U5...EB....m....c3....F....6/...I1.....SF52
...U.qFG9yzb2zzzRYoWzz7lz16.pc..zXCc..kvrEtMc7xD6ocyFE0ujz1..........2.28.kFrA0.
.Ub96aAIVz9.1se7Umvxz0........../EU0.wzzz1...........s/...................E.2c..
zzzz.............0...................2./8.kzzzD............8....................
/EU0.wzzz1...................................2CcN/UvNPcveeWCNq0.yRiibHJJUk1f..XR
SvBmx3CcN/UvNPcvQsLsUa3.ibhVi1bTV1OK.sSq4uCly3CcN/UvNPcvMwLsUa3.ibhVinqTV1OK.sSq
4uCkz3CcN/UvNPcv..EsUa3feeWCNqGQIJ36wk8EwyLsUa3f................................
E....ME/F3U.....I....6....UEZtKNnZ4Jm3aPnNqPmpKA................................
...................../.........E................................................
................................................................................
.....................2.....3..../....6INiJqQdlIRX3KJiB3QcJaQdB4.................
..............................zD................................................
................................................................................
................................/....E/.........0JaPZBLOEZaPZV3.EZ4SZl4.........
........................................U.2.....................................
................................................................................
..........................................E.....I....2....UEZtKNnZqIkVKNmZqM.A4.
...................................................wz...........................
................................................................................
.....................................................A.....3....0....6INiJqQd/JO
iJKAixKKO/.....................................................E..........2.....
................................................................................
................................................................/....E/...U.....
0JaPZBLOI7LMiBbNj7LPo.....................................................2.....
...wz...........................................................................
............................................................................}
{Titel: square}


 
Quote from: DarkBeam on November 04, 2015, 11:55:17 AM
Why redo IQbulb?
Why IQpinetree looks like a tricorn? Probably sign mistake/flipped Cx and Cy?
Accident.  I used IQ for a template for pinetree or something, and I made a mistake, and it was an old version of the bulb (the flat one, shaped like a 2d Mandelbrot).  It might be unnecessary- I don't use it, although it would be good to mix it in if we had one or 2 more formula tabs to play with... then it would add more details.

Quote from: DarkBeam on November 04, 2015, 11:55:17 AM
Some work is needed. And transforms need a _ prefix before too. wink
 K...  I saw that... I just didn't get around to changing them before I got them up.  A bit excited, I suppose.  Apologies.  

Quote from: DarkBeam on November 04, 2015, 11:55:17 AM
PS Have you got a non-trigonometric expansion for IQ formula (even just for power 2)? Would be greatly appreciated!!! Azn

  K...  I will do tomorrow, time for sleep almost!  Original IQ, or one of my mistakes?  I think IQ pinetree was to make a non-z^2 pine tree for higher powers.... to mix with transforms and stuff.  
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DarkBeam
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Fragments of the fractal -like the tip of it
« Reply #58 on: November 05, 2015, 11:15:16 AM »
Oh and I have found this old thread - a cousin of your fractal? The formula is very different though grin (edit not really - almost identical hehe wink )

http://www.fractalforums.com/theory/the-christmas-tree-3d-mandelbrot-set/

 A Beer Cup

Also; I think "_FoldingTetra3D" can be ok as a base for your tetrahedral project... look at it smiley
« Last Edit: November 06, 2015, 12:28:57 AM by DarkBeam » Logged
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M Benesi
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« Reply #59 on: November 05, 2015, 06:21:44 PM »
THATS WHAT HE CALLED IT!!    I thought he called it pine tree....  that's why I kept calling it pine tree... it does look like one a bit.  

  Christmas tree, not pine tree... hahaha...  

  I did switch the y and z coordinates for symmetry (it is slightly more symmetric with y and z switched)....

  I will check ________Folding_tetra_3d... and rename formulas (you can if you have mod editing power) with _ for transforms.  Might need to name transforms something other than T_1 through T_n...


"Note that this code does NOT affect the Menger-type formulas."   For the tetra.  It does affect them if you do it in between unsphere and sphere transforms, but it's not the type of thing I was going for.

  Ohh, and the scale factor for the sphere and unsphere?  Should default to 1 in the formulas to be correct- I thought the sphere was the wrong size, but it wasn't- and it really shows up when you mess with the tetra formula!  That's a quick change in the options!
* _BenesiLucaSpheric.m3f (0.71 KB - downloaded 72 times.)
* _BenesiLucaUnSpheric.m3f (4.06 KB - downloaded 68 times.)
« Last Edit: November 05, 2015, 06:43:05 PM by M Benesi » Logged
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