END OF AN ERA, FRACTALFORUMS.COM IS CONTINUED ON FRACTALFORUMS.ORG

  UPDATE:  For those of you who used the old formulas from this thread, I changed the names in this formula update.  Parameter files that you created using the old formula names will not work with the new formula names.  You can copy the parameters manually by having both formula names in your M3Formulas directory (folder).  

BT1Pine  Pine 1.  The main formula, without bells and whistles.  It's transform 1 then a pine tree Mandelbulb.

BT1Pinegon  Same as above, allows rotations and polygonal transforms in between transform 1 and the pine tree Mandelbulb.  Rotations are before the circle to polygon transform.  If you want to try it in a different order... I'll explain below.

BT1Pinehedron  Similar to the Pinegon, it applies the polyhedral transform after T1 and the rotations, instead of the polygonal tranform.  

BT2Pine  Pine 2.  Transform 2 then a pine tree Mandelbulb.  Combined so you don't have to use 2 formula slots.  Actually, you can use just transform2, instead of transform 2 and the pine tree Mandelbulb (this combined formula) but it's a bit different (of course!).  

BPine_only  Just the Pine Tree Mandelbulb z^2.  Pretty plain.  I use BT1_Transform1, then other transforms, then this with only the x pixel component added in.  

_BPolygonFromCircle     I'm going to update its functionality at some point.  For now, it transforms circles centered on the x axis into polygons.   I'm thinking about putting a rotation (and possibly translation) in all of the geometric space transforms, so that the axis the transform is completed around can be changed (so you can transform stuff around the y or z axes, or any arbitrary axis (vector)).  

_BPolygonToCircle   This transforms regular polygons centered on the x axis with the midpoint of one face on the + y axis into circles.  It reverses the above transform.

_BPolyhedronFromSphere   Transforms a sphere into a polyhedron.  The only regular polyhedron created is a cube, the tetrahedron is stretched along the x-axis (compared to a regular tetrahedron), and the simple way this formula works doesn't allow for multiple face shapes to be generated specifically for the other Platonic solids.

_BPolyhedronToSphere  Inverse of the above transform.  Makes a polyhedron into a sphere.  Works with the Menger to make it into a sphere (if you use it correctly) because the Menger is a cube.  If you want to change the shape of a Menger into another polyhedron, do the above transform, followed by this one (with sides and sides2 both equal to 4), then the Menger (click "repeat from here" in the Menger formula tab).

 _BStellahedronFromSphere   Stellated polyhedrons from sphere.  Still some work to be done, but it works nice with the BT1Pine, sides=6 , sides2=6, angle1~.9, angle2 ~???.

_BRotateFromMag  Rotate the whole coordinate system from the (-1,-1,-1) to (1,1,1) axis, to the x axis (-1,0,0)  to (1,0,0).  

_BRotateToMag   The inverse of the above formula.  Use these formulas if you want to try doing something around the mag axis, and then want to apply it to the pine tree Mandelbulb (BPine_only).  So.. rotate to mag, do your stuff, rotate from mag, pine tree Mandelbulb (BPine_only).

_BSkewXmaxV1  This adds to or subtracts from the x component in various ways, based on various things, to distort the T1 pine tree Mandelbulb fractal types in nice ways.  This formula is not complete, and if I don't get distracted, there will be an update with altered parameters which will be named V2 or V1.1 depending on what I change.


  _BT1_Transform1.  Rotate from x axis (-1,0,0) to (1,0,0), to magnitude axis  (-1,-1,-1) to (1,1,1).  Take absolute value.  Rotate back.  Multiply by scale, subtract offset from x.  Try this by itself, and Luca's switch YZ, if you want to see an asteroid.  Mix it with Mandelbulb or other formulas.  I'll have to add a BJustCoordinates.m3f so you can make a fractal out of just this transform- Mandelbulb 3D won't let you use just transforms to make an object, so if we make a "JustCoordinates" main formula, we'll be able to make things out of just the "transforms"....

_BT1_4D_clampXYZ  4 dimensional transform 1 which preserves the magnitude of x,y, and z so it doesn't introduce as much distortion to 3d fractals.

_BT1_4D_Transform1  4d transform 1.

_BT2_Transform2 makes the fractal "hollow", and gives you lots of neat little connected areas, and what not.  

_BT3_Transform3  Similar to t3, a bit less continuous.

_BT4_Transform4  Similar to both the above.

  Old formulas.rar has the old formula names, if you need them for some reason.  

Thanks for the concise breakdown of the transforms.  If I had only weighted a day, this would have saved me having to piece it together from the original post. LOL.

I sometimes use these transforms in conjunction with other common  transforms  to hollow out  mandelbulbs

// Spherical Offset  (has a  "scale" included to control the size.)
      // Box offset

  hahaha...  I like it for numerous reasons.   

  Tricky...  Luca did it.   And the part you were talking about optimizing is.. probably optimized already in the assembly portion of the code.  The (assembly language) code looked pretty tight to me.  The main slowdown in a lot of formulas is atan2, cos, sin, and the like.  So... ya know. 

  I haven't looked into DE too much- from what I recall, it doesn't like discontinuous functions, which I work with a lot.  That may be the problem.  I don't know the implementation in M3D, so...  I will play more.

     Hmmmm, simplified by Luca the Trickster. That rearranging  maths blows my mind.!!   I am glad I don't have to do it.

Aha, yes! Discontinuous functions, I didn’t think about that.   So maybe there will not be a whole tab devoted to these formulas unless Buddhi  can spare the time.  I only know how to use basic DE.  The only active “real” programmers with Mandelbulber are Buddhi and Zebastian, and they already have a lot to do.  So it is unlikely that I will be able to replicate your amazing images just yet 

Anyway, I am going to code everything up and add it to Mandelbulber (and I want to test it with the MengerSponge).     BenesiMagTransform1 is already  cool in Mandelbulber,  I just have to avoid too much discontinuity.

I have found on the net precise approximations  (eps is 10e-5) of sine and cosine using roundint() that at least in my pc are a lot faster than normal sin(). Interested?
Atan is also approximable

  I don't want to confuse people with too many options, but at the same time, each of the transforms create slightly different fractals.

  If we make the options part of a single transform formula, which allows people to select which transform they want from within the formula, I think the formula will run slower because of the conditionals.  I've run into problems with if/then statements adding a lot of compute time- but I think it might have been the compiler I was using, so maybe doing it in assembly won't create that problem?.

  So we could combine the transforms into one big formula, and then select which one we wanted to do from within the formula menu.

  Ohh, I didn't know you were using Mandelbulber- I must have missed you saying that- I was wondering about the look of the tabs you were posting, I thought you wrote/hacked your own version of M3D.

  I have another formula to port to M3D (having problems with it!  assembly looks right!!  arghh...), but if I can compile code for Mandelbulber, I can probably port these formulas over after I get the stuff I am working on done. 

    Well, these things don't have to be called Mandelbulbs.    We can call them Mandelbulb's redneck cousin, the Mandelbubba. 

  So, here are images from the transforms by themselves (each with their own settings, because they are different).

T1, by itself is a cube... .

T1, with yz switched;  T2 (scale 3.7, offset 1);  T3 (scale 1.7, offset 1.7);  T4 (scale 2, offset 1);
   
   

  So T2 and T4 are very similar (in fact, t3 may be adjustable to be like either!).  In fact... I'm thinking about T4 with different powers for the one part, because of something I saw Inigo Quilez do.


  So.. not sure yet Luca.  Different math is different math- different results are good.  If T2 can be eliminated?? 

Well..  it would be a lot of work to shift stuff around, create a new partition, install Ubuntu, QT creator, etc.  Which I don't mind doing, but not feeling like jumping through those hoops at the moment.  

  If you've got an idea for an easier solution....    You know what.. I'll see if I can grab my dad's old laptop from him and install ubuntu on it.  It's slow...... but it works.  2 computers crunching fractals is better than one anyway, although I think it might be about half as fast as my 8 year old notebook that I'm working on now.  


  So I made a rotate to mag, and rotate back transform.  So you can do a Bulb, rotate to mag, do something along the lines of absolute value like one of the transforms, or maybe amazing box with absolute value or something, then rotate back.  

  What is weird is.. well, you'll see.
 

  So the rotated one (I rotated and rotated back) change colors!  I'm wondering how M3D calculates colors... which I haven't explored yet.