Mandelbrot fractal with punctured points

[forth]

I am using an exotic complex-space theory from maths.ru (sorry no English translation of this work) for drawing of Mandelbrot-4D fractal projection on plane.
Here some complex-space theory definitions:
z=A+jB, where A=w+ix, B=y+iz, i^2=-1, j^2=-1, ij=ji=k, k^2=i^2*j^2=1
abs definition:
||A+jB||=sqrt(|A^2+B^2|)=sqrt(|w^2-x^2+y^2-z^2+2i(wx+yz)|)=sqrt(sqrt(w^4+2w^2x^2+x^4+2w^2y^2-2x^2y^2+y^4+8wxyz-2w^2z^2+2x^2z^2+2y^2z^2+z^4))
I am browsing Mandelbrot fractal in other "dimensions" using rotation ((w+ix)*exp(i*g+j*h), where g - real, h - complex number)
When argument of h is near pi/2 and, radius of h > 3,6 then fractal has chaotic punctured points on iteration edges. because of ||z||=0 and w, x, y, z are absolutely very big numbers.
Some drawings:





P.S. Sorry, English isn't my native tongue.

[hobold]

This is just a guess, but if the absolute values are growing really huge during the computation, you might be seeing artifacts caused by numerical errors. Either because you are overflowing the range of values that the computer can represent, or because of the dynamic range (i.e. the quotient of largest to smallest magnitudes) being larger than the numerical precision.

Remember, real numbers in a computer are usually approximations, and they don't always behave like their abstract mathematical siblings.

[forth]

hobold, you're right. I get overflow on these points
Sorry for this stupid topic 

[hobold]

There are no stupid questions. It's just that some of us have made the same mistake earlier than you.

[cKleinhuis]

indeed

but it show some interesting property, through the chaotic nature of the iteration loop, the distribution of these dots are "chaotic" and should as well show some propabiolity distributions for the iteration bands ... just embrace your problems  

but they arent "stable" meaning that if you scroll the do not "move", they rather flicker ..... and you cant zoom into

btw, did i mention i love double precision gpus ?!

[fractower]

The definition of magnitude seems a bit off since it creates the possibility for heavy zeros (as you pointed out).  I think this disconnect between the magnitude of the components and the magnitude calculation used for bailout is probably the primary cause of the chaotic noise rather than round off.

Try the following magnitude definition.

|A + jB| = sqrt((w-z)^2 + (x+y)^2)

[forth]

fractower, your magnitude definition is even worse produces cases of overflow. Chaotic overflow points are produced on even smaller rotation angles. But anyway thank you)

I have changed order of calculation of magnitude function (sqrt(sqr(w^2-x^2+y^2-z^2)+4*sqr((wx+yz)))) and it is produces less overflow points.
New sample with bigger rotation magnitude:
(view at j-angle h=18*exp(i*pi/2))