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Author Topic: Formula suggestion.  (Read 954 times)
Description: When there will be a time;)
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Alef
Fractal Supremo
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Posts: 1174



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« on: July 31, 2012, 04:03:24 PM »

I think I found noteworthy formula.
Idea is like abox, but julia sets are very dissimilar, and mset alsou are different, throught my abox alsou was a bitt non ordinary. 4 variables IMHO is enought and here alsou negative min Radius values can be used. Only negative trait is strong dependancy on bailout value. I coined the name "baguabox" becouse sometimes it looks like bagua on korean flag and becouse then in my file it stands second after amazingbox;)

Mset:

Some side zoom:

Julia set

(My monitor have some problems with red colour.)

Code:
Baguabox (quaternion) {

// Mandelbox alternative.
// By Edgar Malinovsky 25.07.2012.
// don't forget credits.

parameter real bailout;
parameter quaternion julia;
quaternion C;
real zx, zy, zz, temp, modulus, radius;
parameter real add, Min_R, Scale, lenght;

parameter int settype;

void init(void)
 {
     if (settype=="Julia Set")
    {
z = pixel;
C = julia;
    }
    else
    {
z= 0;
C= pixel;
    }

}

void loop(void)
{
zx=real(z);
zy=imag(z);
zz=part_j(z);



 //Folding by pow 8 modulus having unit circle shaped as octagon pillow.

modulus =((zx)^8 + (zy)^8+ (zz)^8)^0.125;

if (modulus != 0)
{
if (zx > lenght)
{
zx=-zx/modulus -add;
}
else if (zx < -lenght)
{
zx=-zx/modulus +add;
}

if (zy > lenght)
{
zy=-zy/modulus -add;
}
else if (zy < -lenght)
{
zy=-zy/modulus +add;
}

if (zz > lenght)
{
zz=-zz/modulus -add;
}
else if (zz < -lenght)
{
zz=-zz/modulus +add;
}
}


//spherefold. Similar to TGlads original, but allows to use a negative radius.

radius =sqr(zx) + sqr(zy) + sqr(zz);

if (radius < abs(Min_R) )
{
temp = Scale/Min_R;
}
else
{
temp = Scale;
}

//generating z value.

z = quaternion(zx, zy, zz, 0)* temp + C;

}
bool bailout(void)
{
return(  |z| < bailout );
}
void description(void)
{
this.title = "Baguabox";

bailout.caption = "Bailout Value";
bailout.default = 15.0;
bailout.min = 0.5;

    settype.caption = "Set type";
    settype.enum = "Mandelbrot Set\nJulia Set";
    settype.default = 0;

separator.label1.caption  = "Shape depends on folding parameters and bailout.";
  add.caption = "Add value";
add.default = 0.1;

lenght.caption = "Lenght";
lenght.default = 1.8;

Min_R.caption = "Radius";
Min_R.default = 0.5;

Scale.caption = "Scale";
Scale.default = 1.5;

    julia.caption = "Julia Parameter";
    julia.default = (0.35,-0.35,2.3,0);
    julia.hint = "4th value is not used";
    julia.visible = (settype=="Julia Set");
}
}

p.s.
More about this in here:
http://www.fractalforums.com/new-theories-and-research/new-3d-pattern-box/
The same here:
https://sites.google.com/site/3dfractals/baguabox
And at the bottom of my formula file:
http://www.chaospro.de/formulas/display.php?fileid=222

Edited: changed spherefold, so result is wqithout messy regions.
« Last Edit: August 12, 2012, 11:34:51 AM by Asdam » Logged

fractal catalisator
Alef
Fractal Supremo
*****
Posts: 1174



WWW
« Reply #1 on: August 05, 2012, 06:34:15 PM »

Maybe aslou this, throught of corse it would have more niche use:
http://www.fractalforums.com/new-theories-and-research/imho-reason-behind-no-3d-mandelbrot/



https://sites.google.com/site/3dfractals/discussion

Don't know, but power 4 shape is funny:


And an inside rendering:
« Last Edit: August 26, 2012, 04:38:12 PM by Asdam » Logged

fractal catalisator
Alef
Fractal Supremo
*****
Posts: 1174



WWW
« Reply #2 on: September 23, 2012, 07:10:44 PM »

Probably most of folks had seen this.
http://www.fractalforums.com/theory/an-old-formula-revised/msg52114/#msg52114
But anywhay, it is pretty cool fractal.




« Last Edit: September 23, 2012, 07:14:07 PM by Asdam » Logged

fractal catalisator
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