Print Page - Rotation Matrix Mset

A little more computation... for the same thing. :D Will this allow a different approach to the bulb? Yes. Will it be better? Know. <-- it's a pun, figure it out
Better code:

Code:

//  sx and nx are x variables...
//  sy and ny are y variables...
//  r1 is the new magnitude

				theta=atan2(sx+flip(sy));
				r1=(sqr(sx)+sqr(sy))^(n/2);
				
				nx=r1;   //just set them to the magnitude
				ny=-r1;   // this has gotta be negative, or else you get a rotated Mset

			// the + pi/4 is to correct rotational drift for all n... try it without

				sx=nx*cos(theta*n+pi/4)-ny*sin(theta*n+pi/4);
				sy=nx*sin(theta*n+pi/4)+ny*cos(theta*n+pi/4);



// test bailout, repeat...

In 3d, doing something very similar leads to the "Spun Mandelbrot" of yore. I know this has all been said before, but I'm thinking about it now, and mentioning it might spark an idea in someone....

After applying a 3d rotation matrix (http://inside.mines.edu/~gmurray/ArbitraryAxisRotation/) (thanks Glenn Murray, for doing the work!), rotating about the vector (http://en.wikipedia.org/wiki/Euclidean_vector) (0,z,-y), you end up with the spun Mset:

new x= x^2- (y^2+z^2)
new y= 2*xy
new z= 2*xz

To get the vector (http://en.wikipedia.org/wiki/Euclidean_vector) to rotate around, I made the assumption that we rotate from the x-axis to the point (x,y,z), so took the cross product (http://en.wikipedia.org/wiki/Cross_product) of the x-axis (1,0,0) and (x,y,z).

When you do the standard 2d Mset, you rotate around the vector (0,0,-y), which happens to be the same vector you'd rotate around if z=0..... :p

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Fractal Math, Chaos Theory & Research => Mandelbrot & Julia Set => Topic started by: M Benesi on June 02, 2013, 12:44:55 AM