Welcome to Fractal Forums

Thank you Luca! I am looking forward to trying out your new formulas!  ;D

Me too!!  O0

I'm hardly keeping up updating M3D :jabbering:

The next challenge will be finding time to test them...

But nevertheless: Keep them coming Darkbeam!

And i thought i would be the only one  :rotfl:

Surely do :lol:

Thank you so much for sharing those formulas with us Darkbeam !

thanks for all the hard work all of you do and especially to Jesse

Many thanks for all these fascinating new Adds Luca.
Just have to find some time now to explore them properly!  :dink:

Can you make a newton formulas
 z= z- f(z)/f'(z)  Z in Complexes or Z in quaternions
Tank you

Too bad Newton formulas are not convergent so they won't work properly for this program. :sad1:

 Can you make a formula like Z power q +c but q in Quaternions q=a+ib+jC+kd
a,b,c,d in Real
Thank you for all you done

My dear I was planning to do this but I fear this is far too complex and almost useless. Why?
2D fractals with complex powers are all weird looking, because complex part of the power screws up the shape making it non-symmetrical. I have never (never!!!!) seen a fractal with a complex power in any artistic site. So why try to extend this in quat? A really hard work for nothing - nobody will ever use this. If you need to raise a quat to a neg power (-1) you can use sphereinv that already gives beautiful results. I will extend that transform soon. Also, raise to a fractional power is useless due to non-symmetry. :sad1:

raising quat to a quat power;

a ^ b = exp ( b log(a))

1 step: calculate the log of the x,y,z,w quat. It requires four calculations, each one with four + four terms. You cannot do this saving variables at each step but saving at the end :-\ a lot of time to write and very error-risky! I don't have the log fmla already written, so I should write it by scratch! Ouch!!! (well, probably it will require even more steps. I am making an optimistic prevision ;D )
2 step: Multiply by the quat containing bx,by,bz,bw. I fear this is almost impossible without using additional storing bercause fp stack size is only 8 and I cannot exceed it! I must do all computations and then save
3 step: calculate the exp of the previous quat. Other very hard step.
4: Assign previous values to w,z,y,x... easy :)

Another transform that I wish to do is Mobius in 4D; but I am not able because I need more than 4 slots and I don't know how to do! :sad1:

Please for now use what is already done... ^-^

This example: Mset raised to .5 power.

Useless, because the formula is discontinue and fragmented (like Barnsley but less regular) :sad1:

Raised to (0,1) power. Still want to extend this crap to quats? :dink:

you can use dfree1+2 and deriv2+3 are not used yet:

    Dfree1:     Double;     //+216
    Dfree2:     Double;     //+224
    Deriv1:     Double;     //+232    for 4D first deriv or as full derivs
    Deriv2:     Double;     //+240
    Deriv3:     Double;     //+248

Darkbeam did say:

You need to look at more fractal art ! Not to mention the fact that many Mandelbulbs are full of discontinuities and many of the 3D mixed formula types have discontinuities and are also asymmetrical ;)

Why so against storing to memory ? I realise it does cause a slight speed hit, but nothing like as much as having to do a divide or transcendental function using the fpu :)


Don't forget that for quaternions really you should give the user the option of either the above or of:

a^b = exp(log(a)*b)

Since the results will be decidedly different if both a and b have 2 of their last 3 components non-zero.

This video of mine is made out of a complex-power formula:

http://www.youtube.com/v/HFl-pXJOeho?fs=1&hl=es_ES

Also my profile pic:

(http://hphotos-snc4.fbcdn.net/135659_1691284291799_1528504553_1680014_6555946_o.jpg)

Darkbeam did say:

Quote
My dear I was planning to do this but I fear this is far too complex and almost useless. Why?
2D fractals with complex powers are all weird looking, because complex part of the power screws up the shape making it non-symmetrical. I have never (never!!!!) seen a fractal with a complex power in any artistic site. So why try to extend this in quat? A really hard work for nothing - nobody will ever use this. If you need to raise a quat to a neg power (-1) you can use sphereinv that already gives beautiful results. I will extend that transform soon. Also, raise to a fractional power is useless due to non-symmetry


Useless, because the formula is discontinue and fragmented (like Barnsley but less regular)

-------------------------------

Interesting discussion we have going here. Janet Parke is a very well known fractal artist and has won many awards. For several years she also taught a 3 part course on fractal art. One of the points she repeatedly made is that symmetric images are something to avoid. Really good fractal art usually has something to break up the symmetry. This is actually a principle that is true of art in general.

The Glynn fractals use a fractional power for the Mandelbrot set, and they can create marvellous images. One of my older fractal images is a Glynn fractal which has won awards, has appeared on a magazine cover and a poster, and made some money for me.

The logo at the top of my webpage is a negative mandelbrot:

z = (-z)^power + c

where the power is 1.1

I would way that fractional powers are far from useless. If you want to see the logo my website address is

http://www.hiddendimension.com

While we are on the topic of using something other than simple integer powers, I thought I would put up an illustrative image. My 3D Fractal Raytrace formula, which handles a number of different object types, was originally designed for quaternions. Here is a Julia quaternion taken to a quaternion power, namely (3, 0, -1, 0). It also has a coloring texture applied using a variant of Sam Monnier's SFBM II algorithm. I call the image Outpouring.

Okay, maybe I will do that, but not now... Let me take my time :angel1:

Please can you send me this formula (the Mset only...) in a private message? :dink: Only the part that computes new x,y,z,w starting from x,y,z,w,Cx,Cy,Cz,Cw ^-^

I know David, but for example Barnsley is

z = (z+-k)*c

And I would have to do also

z = c*(z+-k)

Too complicated :embarrass:

;D Ty!!!!!!!!!!!!!!

http://www.physcip.uni-stuttgart.de/phy11733/quat_e.html

look a this adresse a old programme called Quat make A^B in the quaternions
it is only for help
Tank you for all you done

void q_exp(point c, const point q)
{
   static double n, f, ex;
   n = sqrt(q[1]*q[1] + q[2]*q[2] + q[3]*q[3]);
   ex = exp(q[0]);
   f = ex*sin(n);
   if (n != 0.0) f /= n;

   c[0] = ex*cos(n);
   c[1] = f*q[1];
   c[2] = f*q[2];
   c[3] = f*q[3];
}

void q_log(point c, const point q)
{
   static double n, f;
   n = sqrt(q[1]*q[1] + q[2]*q[2] + q[3]*q[3]);
   if (n != 0.0)
   {
      f = atan2(n, q[0]);
      f /= n;
      c[0] = 0.5*log(q[0]*q[0] + n*n);
      c[1] = f*q[1];
      c[2] = f*q[2];
      c[3] = f*q[3];
      return;
   }
   else  /* special case: real number */
   {         
      c[0] = 0.5*log(q[0]*q[0]);
      c[1] = atan2(0.0,q[0]);
      c[2] = 0.0;
      c[3] = 0.0;
      return;
      /* comment on asymmetry in i, j and k:
         e^(i*pi)=-1 && e^(j*pi)=-1 && e^(k*pi)=-1
         [ and even linear combinations of i, j and k give:
           e^(a*i+b*j+c*k) = -1 for every a, b, c E R with:
           sqrt(a^2+b^2+c^2) = pi  ]
         the above means that there is an infinite number of solutions to ln(-1).
         Practically, one must choose one of them and thus break symmetry.
         [ Even then there still is an infinite number of solutions due to
           periodicity of sin and cos... ] */
   }
}

void q_pow(point c, const point a, const point b)
{
   /* if a == zero: exp(-inf*b) = 0, if b>0;
      exp(-inf*b) = inf, if b<0
      if b isn't real, exp(-inf*b) isn't defined, because
      lim sin(x) for x->-inf (same with cos) doesn't exists */
   static double an, bnp;
   static point p;
   an = a[0]*a[0] + a[1]*a[1] + a[2]*a[2] + a[3]*a[3];
   bnp = b[1]*b[1] + b[2]*b[2] + b[3]*b[3];
   if (fabs(an) < 1E-200 && (b[0] > 0.0 || bnp != 0.0) ) {
      c[0] = 0.0; c[1] = 0.0; c[2] = 0.0; c[3] = 0.0;
      return;
   }
   q_log(c, a);
   q_mul(p, c, b);
   q_exp(c, p);
   return;
}

I must write both functions directly in assembly, really hard stuff! :sad1:

The formula is really slow and obviously fuzzy, but the overall result is not bad! What look weird in 2D often looks pretty in 3d. :D
I will try to make it ;D

DarkBeam,

A few messages ago you asked for the M-set code. My 3D Fractal Raytrace program is a raytracer that is several thousand lines of code, and uses an extensive  Quaternion math library. All of the fractal objects are plugins into the raytrace program and rely on other libraries that have also have thousands of lines of code. If you have access to Ultrafractal and the Ultrafractal database, the code is all there and publicly available. To illustate what I mean, here is the code for the Power Mandelbrot Quaternion plugin:

class PowerMandel(Quat) {

public:
  import "common.ulb"
  ; constructor
  func PowerMandel(Generic pparent)
      Quat.Quat(pparent)
    im = (0,1)
    hrotp = exp(im*@hangle*#pi/180)
    hrotn = exp(-im*@hangle*#pi/180)
    m_zri = @zri
    m_zjk = @zjk
    m_mand = true
    m_quat = true
    m_fourth = @fourth
    m_ck = @ck
    power = new Vector(real(@pri),imag(@pri),real(@pjk),imag(@pjk))
    powerd = new Vector(real(@pri)-1,imag(@pri),real(@pjk),imag(@pjk))
   endfunc   

  ; calculates the fractal value
  func frcalc(complex &zri, complex &zjk)
    CtoV(zri,zjk,in)
    QH.QPower(in,power,out)
    VtoC(zri,zjk,out)
    zri = hrotn*zri + hrotp*m_cri
    zjk = hrotn*zjk + hrotp*m_cjk
  endfunc

  ; calculates the derivative of the fractal
  func drcalc(complex zri, complex zjk, complex &zrid, complex &zjkd)
    CtoV(zri,zjk,in)
    CtoV(zrid,zjkd,ind)
    QH.QPower(in,powerd,in)
    QH.QMul(in,ind,out)
    QH.QMul(power,out,ind)
    VtoC(zrid,zjkd,ind)
    zrid = hrotn*zrid + 1
    zjkd = hrotn*zjkd
  endfunc

protected:
  complex hrotp
  complex hrotn
  vector power
  vector powerd


default:
  title = "Power Mandel Quaternion"
  heading
    text = "Uses quaternion mathematics."
  endheading
  heading
    text = "z = zr + i*zi + j*zj + k*zk"
  endheading
  heading
    text = "where i, j and k are the imaginary vectors. Multiplication is \
            noncommutative and the inverse of any nonzero element is unique."
  endheading
  heading
    caption = "Mandel Initialization"
  endheading
  heading
    text = "The 'r-i plane' is the traditional complex plane. The 'j-k plane \
            contains the 3rd and 4th dimensions."
  endheading
  complex param zri
    caption = "r-i plane"
    default = (0.0,0.0)
  endparam
  complex param zjk
    caption = "j-k plane"
    default = (0.0,0.0)
  endparam
  heading
    caption = "Quaternion Power"
  endheading
  complex param pri
    caption = "r-i plane"
    default = (3,0)
  endparam
  complex param pjk
    caption = "j-k plane"
    default = (0,0)
  endparam
  heading
    text = "The 'Hart angle' rotates the fractal in the r-i plane. Because \
            quaternian math is noncommutative, unusual shapes and forms are \
            created."
  endheading
  float param hangle
    caption = "Hart angle"
    default = 0.0
    hint =  "The 'Hart angle' rotates the r-i plane. This is not the same \
            as rotating the object."
  endparam
  param fourth
    caption = "4th Dimension"
    default = 3
    enum = "zr" "zi" "zj" "zk"
  endparam
  float param ck
    caption = "4th Dimension Value"
    default = 0.0
  endparam
}

Thanks I am trying to do it "directly" but it's very hard.

Anyway that's what I get for the log of the pixel + int pow... Does not look like normal log transform but that's what I get... If it's correct!

As Dave Makin mentioned earlier there are alternate ways to calculate a quaterionion power since quat multiplication does not commute. Here are the alternate methods I have in my quaternion math library:

; Quaternian power calculated as exp(ln(Q1)*Q2)
  static func Qpower(Vector a, Vector b, Vector c)
;    Q1^Q2 = exp(ln(Q1)*Q2)
;   Find the log of Q1
    float norm = sqrt(a.m_y*a.m_y + a.m_z*a.m_z + a.m_w*a.m_w)
    if norm == 0
      norm = 1e-100
    endif
    complex z = a.m_x + flip(norm)
    z = log(z)
    float at = imag(z)/norm
    float x1 = real(z)
    float y1 = at*a.m_y
    float z1 = at*a.m_z
    float w1 = at*a.m_w
;   Multiply log by Q2
    float dot = y1*b.m_y + z1*b.m_z + w1*b.m_w
    ; calc V x V
    float y2 = z1*b.m_w - b.m_z*w1
    float z2 = -(y1*b.m_w - b.m_y*w1)
    float w2 = y1*b.m_z - b.m_y*z1

    float x2 = x1*b.m_x-dot
    y2 = y2 + x1*b.m_y + b.m_x*y1
    z2 = z2 + x1*b.m_z + b.m_x*z1
    w2 = w2 + x1*b.m_w + b.m_x*w1
;   Take the exponential
    norm = sqrt(y2*y2 + z2*z2 + w2*w2)
    if norm == 0
      norm = 1e-100
    endif
    z = x2 + flip(norm)
    z = exp(z)
    at = imag(z)/norm
    c.m_x = real(z)
    c.m_y = at*y2
    c.m_z = at*z2
    c.m_w = at*w2
  endfunc

; Quaternian power calculated as exp(Q2*ln(Q1))
  static func Qpower2(Vector a, Vector b, Vector c)
 ;    Q1^Q2 = exp(Q2*ln(Q1))
 ;   Find the log of Q1
     float norm = sqrt(a.m_y*a.m_y + a.m_z*a.m_z + a.m_w*a.m_w)
     if norm == 0
       norm = 1e-100
     endif
     complex z = a.m_x + flip(norm)
     z = log(z)
     float at = imag(z)/norm
     float x1 = real(z)
     float y1 = at*a.m_y
     float z1 = at*a.m_z
     float w1 = at*a.m_w
 ;   Multiply log by Q2
     float dot = y1*b.m_y + z1*b.m_z + w1*b.m_w
     ; calc V x V
     float y2 = -z1*b.m_w + b.m_z*w1
     float z2 = (y1*b.m_w - b.m_y*w1)
     float w2 = -y1*b.m_z + b.m_y*z1

     float x2 = x1*b.m_x-dot
     y2 = y2 + x1*b.m_y + b.m_x*y1
     z2 = z2 + x1*b.m_z + b.m_x*z1
     w2 = w2 + x1*b.m_w + b.m_x*w1

 ;   Take the exponential
     norm = sqrt(y2*y2 + z2*z2 + w2*w2)
     if norm == 0
       norm = 1e-100
     endif
     z = x2 + flip(norm)
     z = exp(z)
     at = imag(z)/norm
     c.m_x = real(z)
     c.m_y = at*y2
     c.m_z = at*z2
     c.m_w = at*w2
  endfunc

 ;D Thanks for the suggestions! ps. are you "reb" of the UF database? You are a genius ^-^

The quats in UF database seems to use the bicomplex theory. I use the classic Hamilton theory and for now I prefer to use it for all computations.

Now I succeeded in coding log() and exp(). The problem is that exp(log(Q)) = Q only in a zone near to origin.

So to plot the arbitrary power fractal I must cut off everything outside. :dink: Else, an ugly noise will surround the fractal and the computations will be slowed down. :-\ I hope that this will be enough  :D

I remembered that I asked Jesse for making a test with a complex-power formula, and he had problems because the distance estimation algorithm didn't work well with that. Look: http://www.fractalforums.com/index.php?topic=5252.msg26722#msg26722

That's the 2D section of the sequence. 3D image looks completely wrong,  :-\

This is much better, who knows why? But high powers are destructive :'(

yesssss!!! Now all works fine. I simply replaced some options at the start of each function and everything is correctly plotted :D :D :D :D :D :D :D

Now I only have to write the final formula combining everything in one! O0

Thank you very for all  this formulas Thank you

ERIC

Without your suggestion of the source code of that old program I would never be able to write anything. The base code is very tricky... :-*

can i give you other idea or have you not the time




example: cos(q)=(exp(qi)+exp(-qi))/2   the cosine in quaernions !
            sin(q)= (exp(qi)-exp(-qi))/2

etc .....      the moste difficulte is done
thank you eric

Yesterday I found some quat math libraries. In reality;

sin(a+bi) = sin a * cosh b + i ( cos a * sinh b ) (sine for a complex number)

But in our case;
m = sqrt( w^2+y^2+z^2 )
so x = sin x * cosh m (real part is simple)
but
y = ( cos x * sinh m ) / m * y
z = ( cos x * sinh m ) / m * z
w = ( cos x * sinh m ) / m * w
The division is the tricky part to code ;D
 
(I hope I understood well the cryptic library :embarrass: )
I have all the codings for sinh and cosh already done in assembly ;) ... Will see! ;D (sin S)^2 + C must be a wonderful fractal!

Thank you very much Luca. No words to express the many thanks I have for your dedication to show us The Possibilities Are Infinite. Sorry if I've said that before but it's the same every revision.  :D :dink: :D

You are too kind :D :embarrass:

Finally Jesse told me how to use transforms as pre-transforms!  :dink: :dink: :dink:

I wrote this in the first post, opens an immense field of new possibilities.

I will write new options for (hopefully) all transforms for complete / partial transforms now! ;D

Hello, I'm testing inversions and things on GPU..interessante!! :)
dodeca kifs with invcylindrical-hack
(http://fc09.deviantart.net/fs71/f/2011/065/3/1/luca_on_gpu_by_bermarte-d3b12z9.png)

;D why "hack"? :dink:

Me too  number 752.   :dink: Thanks Luca  :o

Thank you one more time. It's p[en right now and I was looking for a new flare. Gotta try this out.   :D

:ok:

Just wanted to thank you DarkBeam for your formulas.  I'm an artist rather than a mathematician or programmer so I'm grateful to people like you and Jesse for making life more interesting for me.  I'm a great fan of Julias and am starting to explore your new Lambda4Dnc fractal.  I intend to explore it inside out until I'm exhausted!  Nice work!

http://nocache-nocookies.digitalgott.com/gallery/6/3900_14_03_11_10_12_25.jpeg

:o :D :dink:

OMG marvellous work!

Did you try to combine it with 4D functions, like Atan4D, Sin4D... It can be wonderful  O0

I've just started trying combining formulas.  On your advice, I'll concentrate on 4D formulas and see what I can come up with.  Thanks again!   :happy:

Luca, you are totally crazy, there are so many new formulas, it will take years to explore...I love it, keep them coming :D

 :rotfl:  Even more juicy lovelies!  Now where is my psychiatrist?   :rotfl:

Yes, I know... I am totally crazy :D
I make many new formulas because it's so funny :D
Hi there :P

I have done an easy transform that solves once for all the problem of calculating M-sets in warped coord mode.

Simply, use all your transforms, then use the new _updateC as the last transform, with one iteration (needless to say? :dink: ). Then add your favourite formula (you can't render a sequence of transform normally :tongue1: ). Repeat from here: check it in the first formula tab that you use (NOT in the first tab!)

If not understood PLEASE ask, ask! :angel1:

Okay. Example. Used the colors of Popol's last masterpiece (thanks for sharing!). :)


Mandelbulb3Dv16{
N....Es....V1...61.........NQD4flSI2.PT4rKZR8E2EN61imRSKSz9l2YW2tnBwz28xDl5OY5zj
................................XjnTat7cqz1........A./..................y.2.....
.................ME//....6kF1...O/...2E2.....wQPCO1wthpD/..........c./...wX....U
z.EnAnQD....0..........wz........................................y1...sD...../..
.wHnAnQDhX2AbEraYx1..........6DALMhdV1djzl73cXB3CufBHEtenPfIzeLiT8KCQ7qjERXWLvLe
ytP/0c0NtkZMz2Z90cuwq8pj......2q/.....................sD.6kz0...................
.............................UJRR4.wppN.6OLb/.mRR4.irpN.EVLb/UCSR4..............
................E.........UU.g5.7....26...EB....F2...o5....3....m....k11...UiuPI
..kI40XBuwDU.0sz7M./z1V03s8.1c..yhtm.cQVjiO8eGyjBQwRAgHzmz1..........2m78..lE9D.
fsAueCNb..Ym3yuedc8/.1........../6U0xPqVA0EiBV8/2i20.XF92FpyVY.E7UD6HyVzgzP.FcEz
4NqQ.6UkKZMxkayjtodIWOorVyvkhw1ZBGouzKF.8wDJ030.8B6ewXyKUzXbbFpvWtc6.l4zvm1FFj1E
3EU00U5GZ.EBK2Ean0HxzGPFm0nvAI.kddPEmLBlt.2...Ak.1Ugm89.fU.U.06.ZE07.gG4.1Ak.QU/
4..mk.Ak.1.KLR3.h7ozxrD.o7bQ.I7I.06U.cLSt/kcSdTys1E5Ro/.xR4k.1A.wm9j.IbQ.06U..rP
j/.Xz/Ak.1EdYG8....crI0.zzFoTu2.yzngi84.xzZX.45..IaMUELNoJ46YJ46XVa9e/rN..UOkR4.
E....A....E.....I....I....kLkxKOiBKMmJ4.n/....................................U.
...................sz..............................wz..........E........oz1.....
..cF./.......E0E.....................MD8Qxckp1.ED8QxckpXWz1.....................
.....................2.....3.........wJRkFKMoJqE.wqRZ75.g/......................
8.............................0E........kz9.....................................
................................................................................
................................/....E/...E.....1xqQdtKNExqRm..Km...............
........................................kz1.....................................
................................................................................
............................................}

Mmmmh, that's becoming pretty complex.
Btw do you have an example for the P_tree please ?

You dare ask... ;D ;D ;D Now see this abomination ;D


Mandelbulb3Dv16{
N....Es....V1...61...................1.......s1E................................
................................OaNaNaNaty1........A./..................y.2.....
.................ME//....6kc0...u....2E2......NKEvc97VtD/..........c./...w1....U
z.EnAnQD....0..........wz........................................y1...sD...../..
.wHnAnQDMpdv/AOluyf.mpbKpwsuzkEwKRDLIzxjou8riS9R8zflmShm4cVrz2UCIUzDohyDX4TaO5H6
jzHpyBQlHF8mzoSqyQC5x/wD......oy......................sD.6kz0...................
.............................UJRR4.wppN.6OLb/.mRR4.irpN.EVLb/UCSR4..............
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That's really funny, I get 2 totally different pictures in the 3D navi and in the main render. Probably a problem of zoom/scale.

I also noticed that! Really don't know why! Lol
A problem of distance estimation, also noticeable for low raysteps
The atypical type of this map ?

I already discovered by myself how to use transforms as pre-transforms and now I'm able to use them with "KaliLinComb".

Thanks for all the formulas and transformations you made, Luca. I also think you are totally crazy, wich is good for all of us, off course :)
Sorry for complaining in that post about the transformations not working with my formula (it was a joke anyway).

I really appreciate the work you and Jesse are doing with this great piece of software, and for giving the results of your efforts to us without looking for any profit.

 :beer:

That makes the 3D navi totally impossible to use with the P_tree. what a shame :( this function was so promising. Anyway, I did this image: http://www.fractalforums.com/index.php?action=gallery;sa=view;id=6312

No, if you use the fixed step mode you can use it as normal. Only be careful with zoom ;)

Oh yes, I always forget about that. The problem is clipping then, but it's better than nothing.

The problem is because the Rout value is after one main iteration always at 3e60 in the start position and in the nearby positions too!
So there is no gradient and the distant estimate fails.  If you can change something so there is a gradient it might work.

Not sure what you have to change or if you check the vetorlength inside your inner loop already, you might try also to divide by (abs(x0) + 1e-90) instead of testing for zero (is easier too).  But that should not be the main issue because x0 is not zero at that position.

Good luck, really terrific work you are doing!  :)

 ;D

Thanks, will try... But it's not easy manage those toys.

Looking again at IQ-bulb formula I have noticed bad atan coding, now I fixed (well not sure about, I tried all combinations again and... ;D ;D ) - no more branch cut discontinuities and looks prettier. But this formula is hard to manage, some points are hard to understand for me :sad1:

Also I talked with Kali, about his Kalilin...

May you fix it, swapping x-z and cx-cz? If you do so, his formula will support correctly my effects and will work good in hybrid - as is it's almost useless! I don't understand those strange opcodes :sad1:

Uhm, if you do the same swap for Riemann also, ty... The only other one with wrong axis orientation. :)

 A big thank you to all
thanks to you all become possible in the fractals

ERIC

Almost all... ;D

But show us your creations too! :dink: :dink: :dink:

i make examples in the gallery
allways tank you for formulas
a buy a book " geometrie et mesure fractale" i am french ! this book ( very difficult because hard leve in math bac+5 or bac+6 !)
give a lot for expications for fractal as far as we know . But i lerne a lot about it

Tank you

eric

Wooohaaaa, I can't keep up with this tidal wave of formulas!!!   O0
Big thanks anyways BarkBeam, the infinity gets more infinit for everyday thanks to you! (and Jesse of course)  

:beer::beer::beer::beer:

 ;D ^-^ ;D

Hopefully Aexion will help us even more ^-^

Yes it's fantastic to have Aexion on board now ;)

I insisted a bit to encourage him :embarrass:

Thank you Luca! I've got Quadray now. lol Many thanks as always to Jesse and Luca/DarkBeam for all their hard work that has given me so much fun and made me feel like a Mandelnaut!! However, I'm going to forget how to model again by the time I can tear myself away from MB3D. lol

:beer:

Cheers! :D

Thanks a lot for the Koch Cube, a classic that was missing in M3D!

Classic? :hmh: Koch cube is a rare pearl, very few sites host images of it :D and nobody helped me with the formula... and still now it's buggy :'(

Anyway a pleasure :angel1:

appolonius


I you wound how to make circles (spheres) of Apollonius
I think with Mobius but how
thank you for your help
  eric

There is an Aexion formula, enough complicated... :) One day :dink:

Although still buggy ,your with goodies upgraded rare pearl became a high class classic to me already Luca.

Ohh thanks friend. :beer: :dink:

I have a request for the Custom Formula Department.

Is a Lissajous Curve  "_Add" Transform-Type-Thing possible?

I trust my reasons for asking are Obvious  (http://www.sockrateaze.com/carrararama/Smileys/default/smile13.gif)

Here's the wikipedia entry for it : http://en.wikipedia.org/wiki/Lissajous_curve  A few pretty pictures there.  Not as pretty as the Lissa-juous curves on Lissa, but what is?

:D

I would be happy to do this but ... what is the exact formula to implement? And are you sure of it? Please, first test it in a 2d fractal program, then when it's done report it in function of x,y,z coordinates. I will wait ^-^

The exact formula?  Not sure, but variations are on the wikipedia page.  One is (http://upload.wikimedia.org/math/0/1/b/01b180c2cf092b3aca06ce4fc269f851.png)

It has been implemented in Chaos Pro, and may be from UltraFractal's library.

I'll get more details and render an example tonight...

I need a escape time formula that asks xyz, and cx cy cz as input and spits out a new xyz. must converge quickly, preferrably :)

Does a "circly-Koch" ring a bell or did I miss something and is it already available ?

Hey hey, I spent too many hours behind Koch curves for now, later ;D

Anyway, please note that 3D Koch fractals are completely different from UF's 2D ones, due to stricter conformality of transforms. In other words, what is easy in UF is a pain in 3D ;)

Luca

Nothing is easy for me in UF , simply because I don`t have it.

Just found it in UF data base yes and thought  it had some awesome 3d potential.

Enough to learn and explore at the moment so me no complaino  :drink:

Cool new release, DarkBeam!

The SmoothBox seems to work fine, my attempts didn't worked that good, but i tried it always on the sphere folding... could be the reason  ^-^

Just wondering why only 2 Julias if you can have that many (see attached pic and my fomula update)  ;D

Oh please help me :D ...
1. Where do I find the constants in an abox thread? Esi and so on did not work!
2. Damned smooth sphere fold, i was tryin all day but unsuccessfully, looks crappy
Formula is here.
F(R) = k*(r1+rp)/(1+rp)*v+u: R=scale/F(R)
Then x*=r etc ...
Where...
R1 = abs((R-something)/uhm)
K is the sign of R-something :D ... Something should be u, and uhm too?...
Rp = r1**p (int pow for speed. Also exp-1 may be good? )
U = (minr+1)*0,5
V=(1-minr)*0,5
The other constants must satisfy ...
If pow is big, new r must be equal to that you find with standard method.
f(infy)=1 and f(u)=u, and f'(u)=1 (derivate)
Not much time to find the good values :)

Just the same register as the user vars, starting from 0 offset increasing.  For example if you use esi then the first constant is at [esi], second would be [esi + xx] where xx is the size of the first constant, double would be +8.

2. smooth folding...
Thx for the infos, have to test it on the boxfolding, since i never had satisfying results with the spherefolding.
But if you didnt get it to work there either, i think it is a more general problem.

greets

I corrected the formula. You can try it for the sphere folding (it is not for the normal folding, but it should be an approx of the spheric one), but i am not 100%sure of it. Will test again later, but I am sure that your program is correct :)

Updated again the formula... I hope. Internet is not working properly in these days

I just have to thank you once more for the incredible work you do Luca! (And Jesse of corse)  :beer: :beer:
I have found a couple of new favorites in the last version...  O0

 ;D ;D

Cheers! But try also the other ones :)

;D Time!, Time Luca...  ;D