(Mature Content) Bernkastel's thread

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Offline F. Bernkastel

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« on: February 20, 2018, 01:29:12 PM »
This is an advanced render of the buddhabrot formula [z = z^4 + c]
Rendering took 38.8 hours on GTX1060.
Resolution: 8192x8192
Maxiter: 1024
Mandelbrot function calculated: 3.166593e+14 times.



You can download full-size render from deviantart:




Notice small sub-bractals covering the fringe of main circle:




Branches at 60, 180, 300 deg.:



Linkback: https://fractalforums.org/image-threads/25/bernkastels-thread/894/
«...Then clasp me round the neck once more, and give me one more kiss;
And now mine own dear little girl, there is no way but this.»

Offline utak3r

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« Reply #1 on: February 20, 2018, 03:55:56 PM »
That's a damn insane render. Looking quite different than usual, though. Probably due to some different cumulating procedure.

Offline F. Bernkastel

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« Reply #2 on: January 06, 2020, 05:08:58 PM »
Remember Lambert W Function? aka \( z \uparrow\uparrow \infty \). A fun read, if you're interested.
Here is a 16K render, \( c \) from -4.5 to 3.5. Click on image to download in full resolution.

Some notes:
- Actually i rendered it pretty straightforward, \( z_{n+1}=c^{z_n} \), without bailout, simply letting it escape to f32 +infinity, and relying on that, pretty convenient :3
- I've used random sampling method, which is the same as approaching infinite antialiasing. Even though the function is binary (either series converges or diverges), there are gray pixels, indicating highly chaotic small structures.
- Maximum z iterations: 1024.




A bit more of tetration nonsense for you.

lewd one xd
\( z = z * z \uparrow\uparrow 3 + c \)




\( z = z \uparrow\uparrow 4 + c \)




\( z_{i+1}=z_{i} \uparrow\uparrow 16 + c\), where \(i < 128,\ c \in [(-1.5, 1.5i), (1.5, -1.5i)] \)




\( z=z \uparrow\uparrow 100 + c,\ c \) from -2 to 2

« Last Edit: January 07, 2020, 05:34:12 AM by F. Bernkastel »

Offline F. Bernkastel

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« Reply #3 on: January 19, 2020, 10:46:20 PM »
References: https://fractalforums.org/fractal-mathematics-and-new-theories/28/mandelbrot-foam-math/1665

Here is an image with interesting property: at the left side you can see self-similar mandelbrot-like structures, but as you move to the right, it slowly loses such property.

Code: [Select]
/* Not mandelbrot foam */

coloring = orbit_length
MAX_ORBIT_LENGTH = 2048
projection_size = (complex)( 1, 1 );
projection_offset = (complex)( -0.5, 0 );

init {
  complex z = (complex)(1, 0);
  complex c = (complex)(0, 0.5);
  complex w = (complex)(0, 1);
}

loop {
  w = (c * w) / z;
  z = z^2 + w^2 + pixel;
}

bailout {
  return !(isfinite(z.x) & isfinite(z.y));
}



One of those bubbles at right. Despite being fractal, it is not self-similar anymore.

« Last Edit: January 20, 2020, 08:57:15 AM by F. Bernkastel »

Offline gerrit

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« Reply #4 on: January 20, 2020, 04:07:16 AM »
References: https://fractalforums.org/fractal-mathematics-and-new-theories/28/mandelbrot-foam-math/1665

Here is an image with interesting property: at the left side you can see self-similar mandelbrot-like structures, but as you move to the right, it slowly loses such property.

Code: [Select]
/* Mandelbrot foam */

coloring = orbit_length
MAX_ORBIT_LENGTH = 2048
projection_size = (complex)( 1, 1 );
projection_offset = (complex)( -0.5, 0 );

init {
  complex z = (complex)(1, 0);
  complex c = (complex)(0, 0.5);
  complex w = (complex)(0, 1);
}

loop {
  w = (c * w) / z;
  z = z^2 + w^2 + pixel;
}

bailout {
  return !(isfinite(z.x) & isfinite(z.y));
}



One of those bubbles at right. Despite being fractal, it is not self-similar anymore.

You should use old value of w in iteration, or it will not be M-foam.

Offline F. Bernkastel

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« Reply #5 on: January 20, 2020, 08:58:53 AM »
Thanks, i will rename it to not mandelbrot foam then :3

Offline F. Bernkastel

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« Reply #6 on: June 29, 2020, 05:35:52 PM »
Here is my attempt to render menger sponge in Blender, gpu path tracing.
Blend files are in attachment, feel free to play with them ^_^








Offline F. Bernkastel

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« Reply #7 on: June 30, 2020, 05:48:46 PM »
Another variation of the formula.






Orthogonal projection


Offline mclarekin

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« Reply #8 on: July 01, 2020, 10:00:01 AM »
looking good, it is cool to see rendering in blender

Offline F. Bernkastel

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« Reply #9 on: July 02, 2020, 08:52:08 AM »
Sierpinski tetrahedron (crosseye stereo)



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