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Author Topic: Mandelbulber V2.05 extended formulas EXAMPLES  (Read 3251 times)
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DarkBeam
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Fragments of the fractal -like the tip of it


« Reply #15 on: October 13, 2015, 09:23:21 AM »

 cry hello mc wink sorry for hijacking but have you seen these?
http://www.fractalforums.com/feature-requests/new-shapes-in-primitives-cpp/

They should be easy to add and give variety... wink
I have lots of others of course wink
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No sweat, guardian of wisdom!
mclarekin
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Posts: 1735



« Reply #16 on: October 13, 2015, 09:48:33 AM »

yes I remember reading that, and now I am getting to the stage that I can understand some of it. There is so much for me to explore. I havent finished with the trig mandelbuld family, nor tried M.Benesi pinetree modifications. I found my original pinetree code was a  Pinetree just flipped, tried another combination and got  just the mirror image.  Another three  combinations gave me a fractal that crashed the software,  Then I got the three pointer, but have since got distracted.

 Once I thought there was just a small world of standard fractals, now there is an ever expanding universe of fractals.


Cheers
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mclarekin
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Posts: 1735



« Reply #17 on: October 13, 2015, 10:25:36 AM »

@ DarkBeam  BTW this is perfect place for you drop links to previous posts. Then I will have just one place to go and look. grin  Or maybe I should start a new topic called "Help For McLarekin, please give generously" LOL

 In some cases useful information can be hard to find.  Example  the latest pinetree discussion is hidden in a topic called Do M3D formula have to be Distance Estimation formulas?. The discussion that develops within a post can be dissimilar to the topic.  Adding relevant links to a new post gives a better chance of them being easily discovered again. afro



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DarkBeam
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Fragments of the fractal -like the tip of it


« Reply #18 on: October 13, 2015, 11:50:58 AM »

Lol wink I probably need to rename the whole topic (done!)... sorry Matthew (Benesi) smiley
Another great formula author is msltoe - search all his post to find some great formulas lol....

Here I posted many formulas that I consider great... so take also a look!
http://www.fractalforums.com/releases-b233/mandelbulber-v2-2-03/

Good luckkkkk drinking beer together
« Last Edit: October 13, 2015, 12:39:05 PM by DarkBeam » Logged

No sweat, guardian of wisdom!
mclarekin
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« Reply #19 on: October 14, 2015, 01:06:41 AM »

@DarkBeam Thanks, but now my dilemma is choosing what to try next, I am spinning in circles,  being spoilt for choice. I might have to roll the dice to choose.  LOL
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mclarekin
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« Reply #20 on: October 14, 2015, 01:18:28 AM »

About Mandelbulber Extended Formulas

Viewing the iteration loop as a Knight in a 3D chess game. At each iteration loop the Knight moves following a series of transforms (mathematical rules.)  The Knight moves until it either reaches a termination condition i.e. the maximum  number of moves allowed (maxiter) or moves out of the 3D chess board (bail out.)

Some standard fractals are made from two or more transforms.
The Mandelbulb and Quaternion comprise of two transforms. Their Base Formula function produces a sphere, that is modified by another transform ( a type of addition constant)
Mandelbox is simply four transforms:  boxFold, sphericaFold, scale and a type of addition constant.

The fractal formula_extended iteration loop is made up of transforms that can be either :

- single functions, example z = (z + const.A);  where z is changed by a single function, or,

- multiple functions , example z = (z – const.A) - (fabs(z)) + (z * const.B) + (const.C); where the change in z is the sum of a group of single and/or multiple functions.

After each transform the mathematics to create the next new z can be varied by changing parameter variables, including “start/stop at iteration” parameters and even the order of the transforms inside the loop. The possibilities are infinite , but because of render time considerations we have to restrict the number of options.

Example :Transform – Main Rotation.
In this transform we currently have  four  non-integer variables: weight,  alpha, beta and gamma. But weight could be  expanded to weight.x, weight.y, weight.z And each variable could be further modified at each new iteration (by various methods) and can also have a sequence of independent “start/stop at iteration” parameters, constructed to run until termination conditions are met.
Example: run transform for two iterations at five iteration intervals.

Running the fractal formula provides plenty of places to sample the data. With the extended formulas we have many z values:
Initial z,
Final z,
z0, z1, z2 etc; at the end of each iteration until Final z,
And there is a new z after each transform within the loop.

Manipulations of all preceding data can be fed back into the formula at any stage of the calculation. Some of all this data may be also useful with colouring methods,  audio interaction and DE calculations.

To date the extended formulas allow for the construction of only a  few of the infinite possible combinations of transforms, and generally using only the  low overhead functions. 
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Patryk Kizny
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kizny
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« Reply #21 on: October 28, 2015, 04:22:55 PM »

Guys, that's a lot of nice add-ons.
Can you perhaps paste also some of the formulas' pseudo-code?
That would make it easier to implement it in other softwares.
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zebastian
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« Reply #22 on: October 28, 2015, 11:03:33 PM »

You can find the formulas all on https://github.com/buddhi1980/mandelbulber2/blob/master/mandelbulber2/src/fractal_formulas.cpp.
The generalized transforms for the New extended formulas are in .../src/fractal_transforms.CPP

The code is quite self explaining. And tightly bound to the interface.
If you compile the current code base, make settings in the ui and keep an eye in the source code it should be easy to follow the flow
If you have any specific questions i am sure Graeme can help you, Since he wrote most of the fresh extended formulas afro


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mclarekin
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« Reply #23 on: October 29, 2015, 02:05:30 AM »

@ thanks Zebastian


@ patryk

 Patryk

Github  project Mandelbulber has all that has been implemented so far, ( do not look at released V2.05 code). Dev version is beta and may change, but at present  BenesiMagTransformTwo is the only transform not working.

fractal_transfroms.cpp has all the current transforms.
fractal_formulas  has the transform sequence, and some “z” sample points inserted for a color trial in  the last two _extended formulas.

Buddhi and Zebastian have made the layout so simple that even a mclarekin can use it.

Creating the basic Benesi_Tranforms UI took a couple of minutes, (copy previous UI, search and replace old formula name with new, save.  Adding the relevant code  took about 15 minutes, the hardest part was knowing to replace  analiytic DE with Delta DE  for the Bensesi's, (but that is changing those words once, simple). So a new 35 transform formula in less than 30minutes.

It is continuously under- development. So  z sampling  is at its most basic stage like but it is used within the transform loop, and outside the transform loop:.

 
Code:
Image 3) BenesiMagTransformOne is enclosed in an additional transform.
{
previousZ = z;
z =  “Any transform”
z += previousZ * someConstantModifierParameter;
}

Code:
//------------Benesi Transforms --------------------------------
void BenesiTransformsIteration(CVector3 &z, CVector3 &c, double minimumR, int &i, const cFractal *fractal, sExtendedAux &aux)
{
  //boxOffset1
  boxOffsetTransform3D(fractal->transform.boxOffset1, z, i, aux);

  // z sampling for colour trials 0----------------------------------------HERE
  CVector3 sample0 = z;

  //boxFold1
  boxFoldTransform3D(fractal->transform.boxFold1, z, i, aux);

  // z sampling for colour trials 1---BOX FOLD------------------------------HERE
  CVector3 sample1 = z;

  //mainRotation1
  mainRotationTransform3D(fractal->transform.mainRotation1, z, i);

  // z sampling for colour trials 2 MAIN ROTATION----------------------------HERE
  CVector3 sample2 = z;

  // sphericalOffset1
  sphericalOffsetTransform3D(fractal->transform.sphericalOffset1, z, i, aux);

  // z sampling for colour trials 3  SPHERICAL OFFSET------------------------HERE
  CVector3 sample3 = z;

.......

I am still new to coding but I am guessing that creating sample points would have small  overhead. So If I have six sample points, and choose to only use one of them, I would leave them in all place for my next Formula UI.

BTW  I enjoy what you are creating .  afro  I would love to be able to experiment  like you. smiley smiley

Cheers,



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