Mandelbulb - The Unravelling of the Real 3D Mandelbrot Fractal

Skytopia.com ^

[Talisker]

This is a picture of the whole Mandelbrot Set in 3D - mathematically, it has an infinite boundary. The article & pix are explanations and amazing closeups of it.

[tutstar]

Can you post the equation?

[Talisker]

Can you post the equation?

The following is from a referred equation link in the article:

double pi=3.14159265;
double r = sqrt(x*x + y*y + z*z );
double yang = atan2(sqrt(x*x + y*y) , z );
double zang = atan2(y , x);
newx = (r*r) * sin( yang*2 + 0.5*pi ) * cos(zang*2 +pi);
newy = (r*r) * sin( yang*2 + 0.5*pi ) * sin(zang*2 +pi);
newz = (r*r) * cos( yang*2 + 0.5*pi );

Since in the standard Mandelbrot forumla, the only multiplication is the number multiplied by itself (the square), that's why there's only x, y and z in the above function, and not x2, y2, and z2 aswell. Hope that makes sense.

The addition function for these 3D numbers is as expected:
newx = x1 + x2;
newy = y1 + y2;
newz = z1 + z2;

The main Mandelbrot formula stays the same ("a" and "point" are 3D numbers of course - X, Y and Z):
add( multiply(a,a) , point).

Oh and the escape condition is slightly extended over the 2D version like so:
while (x*x + y*y + z*z < 2.0)

[martin_fierro]

[LibFreeOrDie]

Looks like something a mathematical knitter might tackle:

http://www.toroidalsnark.net/mathknit.html

[tutstar]

wow that is over my head! LOL

[martin_fierro]

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[tutstar]

Martin, I just checked and there is no Mandelbrot Sock Knitting thread! 8^)

[Ramius]

Whoa. That rocks.

I think it would be fun to open a bratwurst dog shack called “Mandel Brats”

Whuttyathink?

[Ramius]

Isn’t the idea of “the whole mandelbrot set” sortof a contradiction in terms?

[mikrofon]

Interesting looking pastry ... does it come in cinnamon?

[rottndog]

Oh...I thought that was a 3d representation of the dumbocrats new health care bureaucracy.

[mnehring]

Get your yang out of that pi cos that’s a sin.

[fhayek]

That is one bad ass f**cking fractal!

[bleach]

Thanks for the link. Another site I can get lost in for hours.. So much for getting a life.

[Talisker]

Isn’t the idea of “the whole mandelbrot set” sortof a contradiction in terms?

[steelyourfaith]

[martin_fierro]

lulz ftw

[JRios1968]

[grey_whiskers]

Like,*PING*, folks.

Cheers!