can someone confirm correctness of uf5 mandelbulb formula?

[cKleinhuis]

hi there,
i am right now for the tvshow preparing a tutorial about what a mandelbulb is, as example i want to develop the mandelbulb formula from standard ultrafractal 5 formula
and i am now ready finished with the formula, but i am unsure if everything is implemented correctly, if somebody could extract slices of various z-values and compare them
to my output ?

i am using triplex definition as defined here
http://www.fractalforums.com/theory/triplex-algebra/

i am just unsure if everything is correct, for example i see large away isles when using exponent 8 and a zslice value of 0.6 but this does not seem to correspond
to standard mandelbulb renderers, or am i just getting it wrong ?

please check!  

Code:

class Tut_1_4_Standard_Mandelbrot(common.ulb:DivergentFormula) {
;
; Object version of Mandelbrot in Standard.ufm.
; Generic Mandelbrot set.
;
public:
  complex func Init(complex pz)
    fPixelx = real(pz)
    fPixely = imag(pz)
    fPixelz = @zslice

    x=real(@start)
    y=imag(@start)
    z=@start2
    ;just return something
    return @start
  endfunc

  complex func Iterate(complex pz)
  float newreal=       exponentiateWithRealX(x,y,z,real(@p_power))
  float newimag=       exponentiateWithRealY(x,y,z,real(@p_power))
  float newz=       exponentiateWithRealZ(x,y,z,real(@p_power))

    x=newreal+fPixelx
    y=newimag+fPixely
     z=newz+fPixelz
    ; just return something
    return pz;


  endfunc

  bool func IsBailedOut(complex pz)
  ; perform bailout test using our local variables...
		return sqrt(x*x+y*y+z*z) > @p_bailout
	endfunc
	
  float func exponentiateWithRealX(float x,float y,float z ,float exponent)
          ; Convert Complex Number z to polar form via:
          float length=sqrt(x*x+y*y+z*z) ; modulus, or simply the length of the number: hello phytagoras!
         if(length==0)
                      length=0.000001
                      endif
                      

          float angle=atan2(x+flip(y)) ; nasty atan2 function that returns the angle of the point from coordinate origin...

          float angle2=asin( z/length)

          ; exponentiate length, just like a normal real number ... when exponentiating it is stretched on x-axis,
          ; in polar coordinates it is stretched along its direction
          float newlength= length^exponent
          ; hence complex multiplication is a rotation, e.g. (0,1i)*(0,1i)=(-1,0) where a 90 degree rotation is performed
          ; we multiply the angle with the exponent ...
          float newangle= angle*exponent
          
          float newangle2= angle2*exponent

          ; now create the complex number from newlength and newangle
          ; using standard sin/cos multiplied by length
          float newreal= (cos(newangle2)*cos(newangle))*newlength
          ;float newimag= sin(newangle)*newlength

          ; create complex number and return, the flip serves as helper to convert the real number to imaginary....
          ; seems to be some compiler problem in uf ... return (newreal,newimag) does an "operator needed" compiler error, dunno why....
          return newreal



  endfunc
  float func exponentiateWithRealY(float x,float y,float z ,float exponent)
          ; Convert Complex Number z to polar form via:
          float length=sqrt(x*x+y*y+z*z) ; modulus, or simply the length of the number: hello phytagoras!
       if(length==0)
                      length=0.000001
                      endif

                         float angle=atan2(x+flip(y)) ; nasty atan2 function that returns the angle of the point from coordinate origin...

              float angle2=asin( z/length)


          ; exponentiate length, just like a normal real number ... when exponentiating it is stretched on x-axis,
          ; in polar coordinates it is stretched along its direction
          float newlength= length^exponent
          ; hence complex multiplication is a rotation, e.g. (0,1i)*(0,1i)=(-1,0) where a 90 degree rotation is performed
          ; we multiply the angle with the exponent ...
          float newangle= angle*exponent
            float newangle2= angle2*exponent

          ; now create the complex number from newlength and newangle
          ; using standard sin/cos multiplied by length
          ;float newreal= cos(newangle)*newlength
          float newimag= (cos(newangle2)*sin(newangle))*newlength

          ; create complex number and return, the flip serves as helper to convert the real number to imaginary....
          ; seems to be some compiler problem in uf ... return (newreal,newimag) does an "operator needed" compiler error, dunno why....
          return newimag

  endfunc

  float func exponentiateWithRealZ(float x,float y,float z ,float exponent)
          ; Convert Complex Number z to polar form via:
          float length=sqrt(x*x+y*y+z*z) ; modulus, or simply the length of the number: hello phytagoras!
      if(length==0)
                      length=0.000001
                      endif

                          float angle=atan2(x+flip(y)) ; nasty atan2 function that returns the angle of the point from coordinate origin...

              float angle2=asin( z/length)


          ; exponentiate length, just like a normal real number ... when exponentiating it is stretched on x-axis,
          ; in polar coordinates it is stretched along its direction
          float newlength= length^exponent
          ; hence complex multiplication is a rotation, e.g. (0,1i)*(0,1i)=(-1,0) where a 90 degree rotation is performed
          ; we multiply the angle with the exponent ...
          ;float newangle= angle*exponent
            float newangle2= angle2*exponent

          ; now create the complex number from newlength and newangle
          ; using standard sin/cos multiplied by length
          ;float newreal= cos(newangle)*newlength
          float newz= sin(newangle2)*newlength

          ; create complex number and return, the flip serves as helper to convert the real number to imaginary....
          ; seems to be some compiler problem in uf ... return (newreal,newimag) does an "operator needed" compiler error, dunno why....
          return newz

  endfunc




private:
  float fPixelx
  float fPixely
  float fPixelz

  float x;
  float y;
  float z;



default:
  title = "Mandelbulb Tut 1_4 - Triplex Exponentiation"
  rating = recommended
  helpfile = "Uf*.chm"
  helptopic = "Html/formulas/standard/mandelbrot.html"
  param start
    caption = "Starting point X/Y"
    default = (0,0)
    hint = "The starting point parameter can be used to distort the Mandelbrot \
            set. Use (0, 0) for the standard Mandelbrot set."
  endparam
  param start2
    caption = "Starting point Z"
    default = 0.0
    hint = "Z-Value Starting Point"
  endparam
 param zslice
    caption = "Z Slice"
    default = 0.0
    hint = "Z-Value Starting Point"
  endparam
  param p_power ; Overrides p_power from Formula
    caption = "Power"
    default = (2.0,0)
    hint = ""
  endparam
  float param p_bailout ; Overrides p_bailout from DivergentFormula
    caption = "Bailout value"
    default = 4.0
    min = 1.0
    exponential = true
    hint = "This parameter defines how soon an orbit bails out while \
            iterating. Larger values give smoother outlines; values around 4 \
            give more interesting shapes around the set. Values less than 4 \
            will distort the fractal."
  endparam
}

[cKleinhuis]

and additionally, how do you deal with length=0 special case ?
as you can see i set length to 0.000001 but i think it would be better to just return 0 ?
but 0^0 = 1 ?

[DarkBeam]

but 0^0 = 1 ?

In maths 0^0 is not determined... In a fractal 0 is almost never 0 so it depends on which value you choose

[cKleinhuis]

have you checked the formula ?
btw, google says 0^0 = 1
link

[cKleinhuis]

the problem is that uf5 breaks down if formula creates a division by zero....

[asimes]

I don't have Ultrafractal, but if it helps pow(0, 0) is 1 for me in Processing.

[Sockratease]

http://betterexplained.com/articles/understanding-exponents-why-does-00-1/

 

[cKleinhuis]

dudes has anyone tried the formula?

[DarkBeam]

but try those calculations

0^t
t^t

Where t is a small value. The result is different ... 0 and 1

Btw... when Makin comes back he will help

[cKleinhuis]

yea, makin is easter mässig away ...
but 0^0=1

[cKleinhuis]

or has someone an mandelbulb3d sliced formula that i could use for comparing
@darkbeam  

[cKleinhuis]

i have this slice for triplex z-slice=-0.648993

[cKleinhuis]

but isles are valid
i think it should be ok, although it isnt optimised in any ways

[hobold]

There is no single consistent definition for 0^0. In my experience, mathematicians just choose 1 or 0 as a result, depending on what's more convenient for a particular line of thought. (I.e. not on a line by line basis. But, say, for the proof of a particular theorem, which would consistently use one of the alternatives.)

[DarkBeam]

hi there,
i am right now for the tvshow preparing a tutorial about what a mandelbulb is, as example i want to develop the mandelbulb formula from standard ultrafractal 5 formula
and i am now ready finished with the formula, but i am unsure if everything is implemented correctly, if somebody could extract slices of various z-values and compare them
to my output ?

i am using triplex definition as defined here
http://www.fractalforums.com/theory/triplex-algebra/

i am just unsure if everything is correct, for example i see large away isles when using exponent 8 and a zslice value of 0.6 but this does not seem to correspond
to standard mandelbulb renderers, or am i just getting it wrong ?

please check!  

My holy Saint Spaghetti Codes!!! I tried your formula, I must say I would be very curious to see how it's rendered in 3D...
I was able to run it only after creating an ulb. Another complication!
But I can not understand a row of your damnedly complicated code! The "real" formula is far less complicated than that... 5/6 rows of code and no need of all that commentary.  Please think simpler! Thanks!