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Author Topic: Some Buddha and anti-Buddha fractals + question  (Read 783 times)
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Iariak
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Posts: 26



« on: December 08, 2016, 08:26:21 PM »

Here they are, rendered with my terrifically slow VBA "program". Now the question I have about these is: Apparently these are somehow 3 dimensional? (or maybe even 4 dimensional, not sure) and they can be rotated which makes for a really cool looking animation I'd like to try making.

Now assuming I know how to render these (they are just maps of all the values Z becomes during iterating). Is there a simple way of rotating them? I haven't really found any info on this anywhere. I'm kinda afraid it's gonna be complicated as hell since rotating something in 4D space doesn't really sound all that simple.

Random Buddha Fractal

Anti-Buddha version of the Tricorn
Tricorn Buddha

Anti-Buddha version of the Fountain
Fountain Buddha
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DarkBeam
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Fragments of the fractal -like the tip of it


« Reply #1 on: December 08, 2016, 11:21:57 PM »

Somebody did a 3d buddhabrot render cannot remember who smiley
Welcome btw
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Iariak
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« Reply #2 on: December 09, 2016, 07:02:26 AM »

There are videos of these being rotated on YouTube, I was hoping someone could help with that. Thanks for your welcome  smiley
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Chillheimer
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chilli.chillheimer chillheimer
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« Reply #3 on: December 09, 2016, 09:20:10 AM »

I'Ve been researching into this as well and found the site of the guy who produced the rotated videos, there's quite some info hidden there:
https://benedikt-bitterli.me/buddhabrot/
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knighty
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« Reply #4 on: December 09, 2016, 04:26:51 PM »

Thank you for the link.

It reminds me the excellent work of AluminumStudios here at FF. see for example <a href="https://www.youtube.com/v/y3fwWcV7t0I&rel=1&fs=1&hd=1" target="_blank">https://www.youtube.com/v/y3fwWcV7t0I&rel=1&fs=1&hd=1</a>. and also this and some others in the gallery.
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Iariak
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« Reply #5 on: December 09, 2016, 05:29:33 PM »

Thanks a bunch for the links. Following some of them I found this http://superliminal.com/fractals/bgram/ZrZiOut.htm I am pretty sure all the information I need is hidden in there. I don't know if I can make anything of it but I'll try and hopefully report back x)

edit: I've done it, or at least I think I did. I think I managed to rotate the Tricorn anti-Buddha one. Following the information from the link above, I made these 4 quick renders. Now on the page Melinda Green mentions transformations like ZiZi to ZiCr and ZiCi to ZiCr which I don't understand at all but I think the 4 I have done are correct. I still don't know how to make the rotation gradual to make the animation but I'm pretty sure this is a step in the right direction.
*The ZrZi to CrCi gives the original fractal, I believe if this was a buddha version of the fractal, this transformation would give the exact same image only the white and black inverted.
Tricorn anti-Buddha rotations
« Last Edit: December 09, 2016, 06:35:44 PM by Iariak » Logged
Iariak
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« Reply #6 on: December 11, 2016, 10:41:46 PM »

Alright sorry for bumping this again but I figured everything out and would like to post the result.
Tricorn anti-buddha rotation in 4D
The key information was this (quote from the link in my previous post):

while(z.magnitude() < 2) {
        Z = Z.squared().plus(C);
        incrimentPixel(Z.r, Z.i);
}
to now be:
while(z.magnitude() < 2) {
        Z = Z.squared().plus(C);
        incrimentPixel(Z.r, C.r);
}

This would show the fractal projected on the ZrCr plane (or viewed from the ZrCr plane? I don't even know...). Now to render frames of an animation where the fractal rotates from ZrZi to ZrCr plane you would do something like this

for K = 0 to 1 step 0.1
        while(z.magnitude() < 2) {
                Z = Z.squared().plus(C);
                incrimentPixel(Z.r, Z.i + (C.r - Z.i) * K);
}
next K

That's probably not how you do loops in this language but whatever, you get what I mean smiley
I hope this helps in case anyone didn't know how exactly these animations come to be, thanks to everyone who helped me with this. One last thing I need to figure out is how the planes are ordered so I can make the transitions in the animations more fluid.





« Last Edit: December 12, 2016, 08:10:39 PM by Iariak » Logged
Chillheimer
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« Reply #7 on: December 11, 2016, 10:51:15 PM »

nice to see you're making progress, no need to be sorry to bump, keep us posted!

the buddhabrot perspective on the mandelbrot set deserves more attention.
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--- Fractals - add some Chaos to your life and put the world in order. ---
Iariak
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Posts: 26



« Reply #8 on: December 16, 2016, 05:21:51 PM »

Alright I made one more animation. This time of the Buddha version of the Fountain fractal or whatever the official name is. I believe these are usually referred to as "celtic". I still kinda dislike how the animation goes back and forth because I don't know how the planes are ordered. I just can't make any sense of it. If I wanted to go full circle on one axis, I have no idea how to do that and the program I use to render these is so slow that just trying different orders until I find the right sequence is not really an option cheesy . Anyhow here it is.
Fountain Buddha rotation
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