Perpendicular burning ship - Ring

[Kalles Fraktaler]

Perpendicular burning ship - Ring



http://www.fractalforums.com/index.php?action=gallery;sa=view;id=16761

The search for IFS resemblance in Mandelbrot-ABS fractals continue

Code:

Re: -1.907188768805084171958014934609
Im: -0.00010632394858856694893134255993
Zoom: 6.710880E7
Rotate: 2.373648
Ratio: 1558

[cKleinhuis]

lol, cool stuff you get out of that, aaarrrrh i always foget what you people mean by perpendicular mandelbrot

[youhn]

Does this help?

Code:

// Perpendicular Mandelbrot
else if(m_nFractalType==6){
	if(antal<nMaxIter && test1 <= m_nBailout2){
		for(;antal<nMaxIter && test1 <= m_nBailout2;antal++){
			yr=m_db_dxr[antal]+Dr;
			yi=m_db_dxi[antal]+Di;
			test2=test1;
			test1 = yr*yr+yi*yi;
			if(test1<m_db_z[antal]){
				if(!m_bNoGlitchDetection)
					test1 = m_nBailout2*2;
				bGlitch=TRUE;
			}
			double &r = m_db_dxr[antal];
			double &i = m_db_dxi[antal];
			double &a = Dr;
			double &b = Di;
			double &a0 = dbD0r;
			double &b0 = dbD0i;

			Dnr = 2*r*a + a*a - b*b - 2*b*i + a0;

			double c = r;
			double d = a;
			if(c>0){
				if(c+d>0)
					Dni = d;
				else if(d==-c)
					Dni = d;
				else if(d<-c)
					Dni = -d-2*c;
			}
			else if (c==0)
				Dni = _abs(d);
			else if (c < 0){
				if (c+d>0)
					Dni = d + 2*c;
				else if (d == -c)
					Dni = -d;
				else if (d < -c)
					Dni = -d;
			}
			Dni = _abs((r+a))*b*-2 + Dni*i*-2 + b0;


			Di = Dni;
			Dr = Dnr;
		}
	}
}

Note: don't ask me, I'm not sure either and while I can find the code ... it does not directly help me.

[Alef]

lol, cool stuff you get out of that, aaarrrrh i always foget what you people mean by perpendicular mandelbrot

Perpendicular for pow2 mandelbulb. In one plane there is mandelbrot and in perpendicular plane perpendicular mandelbrot. Realy just a mandelbrot with the reflection symmetric in x axis.

[cKleinhuis]

so, how is the difference to 2d then? by slicing non orthogonal planes ?

[Kalles Fraktaler]

lol, cool stuff you get out of that, aaarrrrh i always foget what you people mean by perpendicular mandelbrot

They are all collected here:
http://stardust4ever.deviantart.com/art/Mandelbrot-ABS-Variations-Complete-Set-of-Formulas-487039852

And cubics here:
http://stardust4ever.deviantart.com/art/Cubic-Mandelbrot-ABS-Variations-Incomplete-487039945

[Alef]

It is the perpendicular cutout of the power2 mandelbulb. It have normal mandelbrot in XY plane and not so in XZ. I can't share the attached image, but it's the last picture
http://www.fractalforums.com/new-theories-and-research/why-there-isn't-3d-12-conformal-transformation/msg66343/

Like adding this z= abs(real(z))- 1i*(imag(z)) after the z+z+c  or somethging like that.

There were a great thread, but images seems to had dissapeared:
http://www.fractalforums.com/new-theories-and-research/complex-not-so-complex/ Or that was the other thread by puntopunto   They both don't have images about reflections and rotations.

[Alef]

You can add to the list Quad Gen by Jos Hedriks (Puntopunto). If you prefare squares over spirals.
x=x^2+y^2+c
y=2.5*x*y+c
or pretty simmilar exept in shape
x=x^2+y^2+c
y=-2.5*x*y+c

or more interesting in zooms with abs
x=abs(x^2+y^2+c)
y=abs(2.5*x*y+c)

Or good old but not very zoomable Talis from Fractal Explorer.
z= z^2/(z + 1) +c  (or z= z^n /(z^ (n-1) + 1) +c )

Or this alsou from FE. Its kind of mandelbrot set with julia sets flying around in every zoom.
z=z*sinh-c^2