Print Page - Unit Vector Mandelbulb (variations)

I was wondering, do 2D mandelbrot variations will work in 3D. Then I downloaded latest tma2.ufm and found just single new formula "Unit Vector Explorer" but with lots of functions instead of original cabs. Original idea was just at every iteration to add some 0.1 of the same sign to the z.
This is pretty easy in quaternion numbers, well, actualy at first it was in quaternion numbers;)
z= triplex mandelbulb formula(z)
z=z+factor*z/ quaternion function(z)

Here is Chaos pro code as uploaded. Chaos pro probably are't the best 3D renderer, but could be one of the best tool for experimenting with formulas;)

Code:


Here goes normal Mandelbulb DE code...

		// now modifaying z insted of triplex
		z=quaternion(sx,sy,sz,0);
		
		if (vectored=="Non Tweaked")
		{
		z=z;
		}

		else if (vectored=="Z/Cabs(Z)" && cabs(z)!=0)
		{
		z=z + coefVector*z/cabs(z);
		}	
	
		else if (vectored=="Z/abs(r)+abs(i)+abs(j)" && abs(real(z))+abs(imag(z))+ abs (part_j(z))!=0)
		{
		z=z + coefVector*z/(abs(real(z))+abs(imag(z))+ abs(part_j(z)) );
		}

		else if (vectored=="Z/conj(Z)" && (z)!=0)
		{
		z=z + coefVector*z/quaternion ( real(z) , -imag(z), -part_j(z), -part_k(z) );
		}

		else if (vectored=="Z/sqr(Z)" && sqr(z)!=0)
		{
		z=z + coefVector*z/sqr(z);
		}	
	
		else if (vectored=="Z/recip(Z)" && recip(z)!=0)
		{
		z=z + coefVector*z/recip(z);
		}	

		else if (vectored=="Z/round(Z)" && round(z)!=0)
		{
		z=z + coefVector*z/round(z);
		}

		else if (vectored=="Z/ln(Z)" && ln(z)!=0)
		{
		z=z + coefVector*z/ln(z);
		}

		else
		{
		z=z+0.0001;
		}
		
		sx=part_r(z);
		sy=part_i(z);
		sz=part_j(z);		
// by Edgar Malinovsky.

First z=z+f(0.2, 1)*z/ cabs(z)
Second z=z+f(-1, 0)*z/ ln(z) :angel1:
Third z=z+f(1, 0)*z/ round(z) This is nice one. Mandelbox meets mandelbulb.
Forth z=z+f(-0.25, 0)*z/ sqr(z)

Round function sculpted the mandelbulb. Like when sculptor cut a granitestone, but left his work undone. Colouring is extremely ugly, but it perfectly shows properties of figure.
z=mandelbulbformula(z)+c;
z=z+ (-1,-1)*z/round(z);

And here is version of rotated mandelbulb. (The same function generates rotated mandelbrot of lkm3.upr)
z=mandelbulbformula(z)+c;
z=z* z/cabs(z);

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Fractal Math, Chaos Theory & Research => (new) Theories & Research => Topic started by: Alef on February 01, 2012, 08:12:08 PM