Benesi "pinetree" (fold+bulb)

[mclarekin]

Hi DarkBeam,  I was telling the truth  :-

My trigonometry knowledge is in the far distance past (not like you guys)  so I just ignorantly made these changes

So I look at Buddhi's mandelbulb code and  think  "This is not the same as in the post " What is arg??? , what is going on with  atan or atan2 and sin or cos ?? I wonder if its a different way of writing the same formula???

So I decided I would just change the x, y, z things,  and not the trig.  Render it to see I would get an image. Then ask at FF if the formula was correct  .

I now suspect it may not be a Pine Tree. Oh well,  So I will make those changes and see what I get  Thanks 

Cheers

[DarkBeam]

That said I tried to put the non-trig pinetree but looks totally different from any image posted as I feared. It is in its pure form here.
The m3f (you can disassemble pasting the code into OllyDbg... the formula starts after the 1st FNOP and FLD QWORD PTR DS:[EBX] loads X into the stack, (...)EDX is Y, (...)ECX is Z, FADD QWORD PTR DS:[ESI+18] adds CX, ebp stuff stores temporary variables... and so on );

Code:

[OPTIONS]
.Version = 2
.DEscale = 1
.SIpower = 2
[CONSTANTS]
Double = 0.816496580927726
Double = 0.5773502691896258
Double = 0.7071067811865475
Double = 2.0
[CODE]
558BEC81EC300000005356578B75088B7E308BD8D9D0DD03D8C8DD5DF8DD02D8
C8DD5DF0DD01D8C8DD5DE8DD03D8C0DD45F0DC45E8D9FADEF9DD5DE090DD45F8
DC65F0DC65E890DD45E0DD45F0DC65E8DEC990DD45E0D8C0DC09DC0A90DC4620
DD1A90DC4628DD1990DC4618DD1BD9D08BC35F5E5B89EC5DC20800
[END]


Description:

Benesi pinetree formula;

xt = x*x; yt = y*y; zt = z*z;
t = 2*x/sqrt(yt+zt);
x = xt-yt-zt+Cx;
z = t*(yt-zt)+Cy;
y = 2*t*y*z+Cz;

[/code]

[DarkBeam]

YEAH!!! It works, I added it to the database! BenesiPine1 (2 is in preparation )
Just, it needed the fold before to work okay...

[M Benesi]

You're good Luca.   If you rotate the image 90° clockwise, what does it look like?  



  Seriously though: you got it right.  You don't recognize it because we switched the y and z components, but this is it here (from my ChaosPro code):



  The viewing angle I use for the render is a bit more narrow, but it's definitely the same formula.  

[M Benesi]

YEAH!!! It works, I added it to the database! BenesiPine1 (2 is in preparation )
Just, it needed the fold before to work okay...

  You are awesome Lucal!@$!@$    Nice job!

  I forgot to tell you about the initialization!!!   You need to treat the fractal like a Julia, sending the pixel value into the formula first!  

  After every Mandelbulb iteration, you ONLY add in the x pixel component, which makes it much more smooth.  You do not add in any pixel component after the other formulas: they are basically pure Julias, using the offsets as the Julia component.

  Adding only the x pixel component is the key to a completely smoothly evolving fractal: it will be much more symmetric! 
 
  If you add in the whole pixel component (x, y, and z) after the Mandelbulb part, the fractal is not as nice looking, although it is still cool.

x pixel only,  full pixel
   

second formula x pixel only,  full pixel:

 


  So you really only want the x pixel added in, to make a nice symmetric fractal, otherwise you get more stretchy sections.

[DarkBeam]

A question;
Which symmetry is that? Tetrahedral, icosa, etc... and can it be made to other platonic solids?...

I know it may become a brain torture

  I forgot to tell you about the initialization!!!   You need to treat the fractal like a Julia, sending the pixel value into the formula first! 

  After every Mandelbulb iteration, you ONLY add in the x pixel component, which makes it much more smooth.  You do not add in any pixel component after the other formulas: they are basically pure Julias, using the offsets as the Julia component.

 
  If you add in the whole pixel component (x, y, and z) after the Mandelbulb part, the fractal is not as nice looking, although it is still cool.

Do not worry... It is enough cool - Initializations may bug the code and not adding all C components is not a good idea because Julia sets would be "forced" to have only infinite^1 variants and not ^3!

[M Benesi]

  Look in the post above yours.    If you're on Facebook, send me a friend request so we can open a chat window.

Be back in a bit...  I need breakfast!  Almost 11am here... did it again.  Time to eat.  

[mclarekin]

I am beginning to understand all of this much better

1) there is a whole family of mandelbulbs to explore simply by changing the trig functions. Hmmmmm?  So I could code a basic mandelbulb formula with enable checkboxes to vary the trig functions

2) and you  use  formulas 1 and 2 as modifiers  produces  these amazing fractals. 

3)  and i know now why it is called pine tree

The infinite possibilities has just increased again for me.

Thanks guys

[DarkBeam]

I am beginning to understand all of this much better

1) there is a whole family of mandelbulbs to explore simply by changing the trig functions. Hmmmmm?  So I could code a basic mandelbulb formula with enable checkboxes to vary the trig functions

2) and you  use  formulas 1 and 2 as modifiers  produces  these amazing fractals. 

3)  and i know now why it is called pine tree

The infinite possibilities has just increased again for me.

Thanks guys

Yeah you should do it! Variations include asin acos atan and atan2.
For each possible coupling of angles... x y z ... etc
I made it in Mandelbulb years ago
Plus! Another topic you should look at ...
http://www.fractalforums.com/the-3d-mandelbulb/iterating-c/

[M Benesi]

3)  and i know now why it is called pine tree

  Because you can hang it from your rear view mirror and it makes your car smell fresh?

  I think Bugman named it Pine Tree, lemme find his website for you, it has a bunch of the formulas written out.   I've found the Pine Tree one produces the smoothest fractals with the various mods above...

  http://bugman123.com/Hypercomplex/

[M Benesi]

That said I tried to put the non-trig pinetree but looks totally different from any image posted as I feared. It is in its pure form here.
The m3f (you can disassemble pasting the code into OllyDbg... the formula starts after the 1st FNOP and FLD QWORD PTR DS:[EBX] loads X into the stack, (...)EDX is Y, (...)ECX is Z, FADD QWORD PTR DS:[ESI+18] adds CX, ebp stuff stores temporary variables... and so on );

Code:

[OPTIONS]
.Version = 2
.DEscale = 1
.SIpower = 2
[CONSTANTS]
Double = 0.816496580927726
Double = 0.5773502691896258
Double = 0.7071067811865475
Double = 2.0
[CODE]
558BEC81EC300000005356578B75088B7E308BD8D9D0DD03D8C8DD5DF8DD02D8
C8DD5DF0DD01D8C8DD5DE8DD03D8C0DD45F0DC45E8D9FADEF9DD5DE090DD45F8
DC65F0DC65E890DD45E0DD45F0DC65E8DEC990DD45E0D8C0DC09DC0A90DC4620
DD1A90DC4628DD1990DC4618DD1BD9D08BC35F5E5B89EC5DC20800
[END]

  Question, where do you drop the code into OllyDbg, or do I need to grab the binary???  [/code]

[mclarekin]

@DarkBeam Thanks for showing me that post.  The simplifications and workarounds blow my mind.   
@Benesi Thanks for that interesting VIBRANT site.

There is so much to learn BUT :

my status early June 2015 (when i was asking Buddhi  to take a gamble and help me play with his source code.)

Status
I have no real experience in programming, the only code I have ever looked at is Mandelbulber, the only coding I have ever done is openCL custom formulas in Mandelbulber (using Notepad), and the only coding I understand is most of the formula code. So I know nothing about terminology and how a trained programmer would do things.

And now just a few months later I  can write transforms in C++ with QT designer and compile & run,  and every day I am learning more

FractalForums has grown so big that it really helps a lot when you guys who have been "around a while" can direct us to relevant old posts.

The possibilities of all the infinities  are ridiculously huge

Thanks again

[DarkBeam]

Code:

[quote author=M Benesi link=topic=22123.msg87695#msg87695 date=1444519054]
  Question, where do you drop the code into OllyDbg, or do I need to grab the binary???  

[/quote]
Open OllyDbg.
Open an exe file ... I use twunk32.exe
Go to the end of file it is all full of 00000....
Binary paste
You will see the source

[DarkBeam]

I get horrible results replacing the fold 1 with the fold 2

Matthew please can you clarify your statement...
How many times - how it is meant to be used

For the top image type, one alternates between formula 1 (below) and the pine tree Mandelbulb formula.  For the second image type, every few iterations one substitutes formula 2 (instead of formula 1) in between the pine tree Mandelbulb formulas.  Initialize the formula with pixel values, and then only add in the x pixel component each iteration, otherwise it isn't as pretty, although it still is the best z^2 type out there.

[M Benesi]

   PT: Pine Tree   F1: formula 1   F2: formula 2

  F1, PT;  F1, PT;  F1, PT;  F1, PT;  F1, PT;

5 combination iterations, or 10 total iterations:

x pixel only,  full pixel
   

 PT: Pine Tree   F1: formula 1   F2: formula 2

  F1, PT;  F1, PT;  F1, PT;  F2, PT;  F1, PT;

with second formula for the "7th" iteration, or beginning part of the 4th combination iteration

x pixel only,  full pixel:
 

  PT: Pine Tree   F1: formula 1   F2: formula 2

  F1, PT;  F1, PT;  F1, PT;  F2, PT;  F1, PT;


  Settings for F2 are ~1.9 and ~1.9.  For F1: they are around 2.  PT is the z^2 version, with only x pixel component added in (do a Julia for experimentation if you want).  


  Formula 2 introduces details to the formula 1 modified PT.  If you start out with F2, you get something more like the following (only 2 or 3 iterations!  it gets chaotic if you apply F2 too often):