Here is another hybrid I am working on that mixes Julia and Mandelbrot sets. The result looks really strange to me. If you look closely, there are other mini-brots in here, far away from the main set in the middle. This is zoomed out pretty far ar radius 10. No msets should be out this damn far! :^o
The code waits for a point to escape then applies one of the jp sets, and reties the iteration this way for 16 times. Then, after that points are finally allowed to escape. Here is the algorithm:
______________________________
int g = 0;
ct_complex jp[2] = {
{ .04, .07 },
{ -.04, -.07 }
};
// iteration
z = z*z + c
if (z.real() * z.real() + z.imag() * z.imag() > 256)
{
if (g < 16)
{
z *= (i % 2) ? jp[1] : jp[0];
++g;
continue;
}
// we really escaped this time...
// color
return;
}
______________________________
___
#Fractal #Julia #Mandelbrot #Hybrid #Art #Space #Math
The code waits for a point to escape then applies one of the jp sets, and reties the iteration this way for 16 times. Then, after that points are finally allowed to escape. Here is the algorithm:
______________________________
int g = 0;
ct_complex jp[2] = {
{ .04, .07 },
{ -.04, -.07 }
};
// iteration
z = z*z + c
if (z.real() * z.real() + z.imag() * z.imag() > 256)
{
if (g < 16)
{
z *= (i % 2) ? jp[1] : jp[0];
++g;
continue;
}
// we really escaped this time...
// color
return;
}
______________________________
___
#Fractal #Julia #Mandelbrot #Hybrid #Art #Space #Math

View 11 previous comments
Apr 20, 2017
I call it 'mulia'. Four steps mandel, rest is +Chris Thomasson's alternating Julia:
http://tinyurl.com/lgmkmfbApr 20, 2017
+Refurio Anachro
You got it! Fwiw, the details inside the disks are created by creating a large number o. Then take the min value of the iterates of z via:
o = min(o, std::abs(z));
We use this to color RGB like, non-escaping and/or escaping:
unsigned char red = (unsigned char)(o * 1234); // cast some red?
we can take the floor of abs(o * 1234), strip off the decimal, and mod it into byte range wrt 0...255.
Now, your Mulia algorithm is really neat Refurio. I will try to recreate it.
Also, the fact that your online explorer has the means to derive my Julia hybrid is really neat!
Thank you. :^DApr 21, 2017
+Refurio Anachro
I am wondering if you are familiar with my crude technique to gain field lines that are different than you average n-ary decomposition in the sense the they are created from actual non-escaping regions.
Check this out:
plus.google.com - I almost have a simplistic, perhaps naive, way to get field lines off of a Ma...
(the first time I made it public...)
http://www.fractalforums.com/new-theories-and-research/plotting-field-lines-during-iteration/
(read all...)
https://plus.google.com/101799841244447089430/posts/YoktF5J94jb
I am going to apply this to the infinite nest of hybrid mutations.
;^)Apr 21, 2017
+Chris Thomasson shared his:
> [method for coloring the inside]
Cool. Thanks! Measuring things like min(abs(z)) during the iteration is a good idea. I wonder if there's a natural way to integrate that into my portrait plotter.
> [simplistic method for field field lines]
This one should be easy.Apr 21, 2017
I just noticed one can get (positive) real field lines that end in a short imaginary segment like this:
z0: zp=p
f(z): (zp=z)²+p
outside:
hsv(0, 0, axes(z/zp/zp))Apr 21, 2017

