Title: Some Buddha and anti-Buddha fractals + question Post by: Iariak 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. (https://c2.staticflickr.com/6/5734/30951109561_ed2832b066.jpg) (https://flic.kr/p/Pa3wy2)Random Buddha Fractal (https://flic.kr/p/Pa3wy2) (https://c1.staticflickr.com/6/5774/30702106760_5a7b8ff935.jpg) (https://flic.kr/p/NM3jGh)Anti-Buddha version of the Tricorn (https://flic.kr/p/NM3jGh) (https://c7.staticflickr.com/6/5670/30614141030_fe52551639.jpg) (https://flic.kr/p/NDgtxL)Tricorn Buddha (https://flic.kr/p/NDgtxL) (https://c2.staticflickr.com/6/5826/25367799289_31b260f6d7.jpg) (https://flic.kr/p/EDEAVP)Anti-Buddha version of the Fountain (https://flic.kr/p/EDEAVP) (https://c4.staticflickr.com/6/5788/30279202123_51a1fa1c7c.jpg) (https://flic.kr/p/N8EPT2)Fountain Buddha (https://flic.kr/p/N8EPT2) Title: Re: Some Buddha and anti-Buddha fractals + question Post by: DarkBeam on December 08, 2016, 11:21:57 PM Somebody did a 3d buddhabrot render cannot remember who :)
Welcome btw Title: Re: Some Buddha and anti-Buddha fractals + question Post by: Iariak 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 :)
Title: Re: Some Buddha and anti-Buddha fractals + question Post by: Chillheimer 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/ Title: Re: Some Buddha and anti-Buddha fractals + question Post by: knighty 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 this video (https://www.youtube.com/watch?v=y3fwWcV7t0I). and also this (http://www.fractalforums.com/index.php?action=gallery;sa=view;id=17787) and some others in the gallery. Title: Re: Some Buddha and anti-Buddha fractals + question Post by: Iariak 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. (https://c8.staticflickr.com/1/238/31533231135_ef1f0edb12_z.jpg) (https://flic.kr/p/Q3u41T)Tricorn anti-Buddha rotations (https://flic.kr/p/Q3u41T) Title: Re: Some Buddha and anti-Buddha fractals + question Post by: Iariak 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.
(https://c2.staticflickr.com/6/5592/30772482533_96795f846c_o.gif) (https://flic.kr/p/NTg1XF)Tricorn anti-buddha rotation in 4D (https://flic.kr/p/NTg1XF) 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 :) 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. Title: Re: Some Buddha and anti-Buddha fractals + question Post by: Chillheimer 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. Title: Re: Some Buddha and anti-Buddha fractals + question Post by: Iariak 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 :D . Anyhow here it is. (https://c1.staticflickr.com/1/281/31645386656_6e61412ee4_o.gif) (https://flic.kr/p/QdoSWL)Fountain Buddha rotation (https://flic.kr/p/QdoSWL) |