### Meet the Twelve Angels

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#### beer

• Fractal Freshman
• Posts: 5

#### Meet the Twelve Angels

« on: May 23, 2018, 06:28:34 AM »
Ever wondered if there is more than one Buddhabrot?
I asked myself the same question, and it turns out there are 12!
I am not sure if this has been done before, but please meet the 12 angels.

Some things are very interesting, for example the change in appearance when conjugating the Mandelbrot formula...
These images also contain astounding details which are hard to describe.  I have some high res renderings (4000x4000), but unfortunately each of them takes more than 5 mb, or 60 mb in total.  Is there a good method for sharing these?

I wish to thank nmmm for creating some code in Java which I discovered while doing research on the matter.  Unlike the other Buddhabrot/Nebulabrot implementations, he uses no random numbers, but just scans linearly through the complex plane.  It turns out this gives rather nice and sharp renderings, resembling x-ray photographs or even holograms.

An idea for the future is to generate colour images, but I did not have the time yet to do that.  Colour or some sort of high definition range mapping will also reveal more interesting details which currently are not visible because either the halo is too bright or the dark areas are too dim.

Update: It seems there is a program which does something related (BuddhabrotMag), but I'm not sure how it works and if it uses the random method or linear scanning because I have no opencl and can't test it right now.

Source code attached.
PS: Probably there will be more variations which still are to be discovered.

#### Sharkigator

• Fractal Friend
• Posts: 13

#### Re: Meet the Twelve Angels

« Reply #1 on: May 23, 2018, 10:13:39 PM »
BuddhabrotMag uses random numbers.
It evaluates random orbits, evaluates how much they influence the image and then mutates and reuses the best orbits.
That allows for quick rendering even when zoomed in.

Also, you can render any variant of the Buddhabrot in Mag, as it supports user formulas.

It seems that AMD does not provide downloads for OpenCL CPU drivers anymore.
For Intel you can get them there: https://software.intel.com/en-us/articles/opencl-drivers#latest_CPU_runtime
And if you've got a OpenCL capable graphics card, updating your drivers manually should work.

#### Fraktalist

• Strange Attractor
• Posts: 916

#### Re: Meet the Twelve Angels

« Reply #2 on: May 30, 2018, 01:31:53 PM »
hey beer, welcome to the forum.

I think what you have discovered yourself is already known.
Ito me it looks like the buddhabrot method display of something like this:
https://imgur.com/Zc3GrWv
variations of the formula.

also: sharkigator is actually the humble programmer of buddhabrot max - imho the best buddhabrot explorer currently out there.
you can find many if not all your examples in the formula dropdown.
Very much worth to give it a try. Let me know if I can help you finding your way around it, it's actually really simple - if you know the first 2-3 steps to generating an image.
I installed that opencl thing (don't remember which exactly, long ago, still running) and it works great and very fast on my radeon graphics card.

#### beer

• Fractal Freshman
• Posts: 5

#### Re: Meet the Twelve Angels

« Reply #3 on: May 31, 2018, 04:06:44 AM »
Yes, my program is exactly calculating what the animation shows, so it is not new in principle.  Only the method of rendering I used is is a bit different, because I did not use random points.
However, after some research on the internet, I am quite sure that at least online you can only find a small subset of the variations I created by systematizing the generating function.
What is puzzling in particular is that most renderings I found are not depicting the variations which resemble angels, as for example the "burning ship" looks more abstract when rendered as a nebula than most of the other variations.
An exception might be the Tricorn rendered as nebula ("Lotus leaf"), but no one seems to recognize it as three female feathered figures...
I also rewrote my program so it uses multi threading, which makes it much faster, and I added the third power (z <- z³ + c), which creates a slightly different set of figures.
I still have to look into the program you mentioned, but I am using Linux at the moment, so I will have to set up my Windows machine again.

Some sites worth visiting on the subject:

http://wee.codes/art.html
https://hiveminer.com/Tags/buddhabrot/Recent
http://yozh.org/gallery/
http://richardrosenman.com/shop/buddhabrot/
http://www.fractalforums.com/images-showcase-(rate-my-fractal)/high-detail-nebulabrot-space-lotus-vs-buddha/

Animations rotating the viewing plane:

It is very striking that at all of them created very beautiful renderings using the nebula method with very sophisticated rendering methods, but no one seems to have made a full set, yet.

Very interesting variations, rendered from real plane (I still have to figure out what he means by "Quasi").
https://softologyblog.wordpress.com/2016/09/18/custom-formula-editor-for-visions-of-chaos/
It seems that the higher powers/orders might look more and more human/animal like.

#### Fraktalist

• Strange Attractor
• Posts: 916

#### Re: Meet the Twelve Angels

« Reply #4 on: May 31, 2018, 12:34:00 PM »
wow, thanks for those rotation youtube videos, hadn't seen any like that before!
spacelotus is really incredible!

as much as I enjoy the full views of different formula variations, I am more interested in the details that this method shows.

I think everyone sees different things, depending on the background. It's mostly pareidolia so I try to not give too much meaning to it. It just looks great, and having observers see different things in images/art is a good thing.

#### hgjf2

• Fractal Fanatic
• Posts: 27

#### Re: Meet the Twelve Angels

« Reply #5 on: June 02, 2018, 11:56:55 AM »
Twelve angels!
Normally that fractals that's are named BUDABBROT that are the shape of Nirvana.
Those really look like the angels, exact how was been described in the witnesses from afterlive realm, at cases of  the Lazarus syndrom.

#### wes

• Fractal Friend
• Posts: 13

#### Re: Meet the Twelve Angels

« Reply #6 on: August 25, 2018, 09:12:49 PM »
I think what you have discovered yourself is already known.
Ito me it looks like the buddhabrot method display of something like this:
https://imgur.com/Zc3GrWv
variations of the formula.
I created that animation. Thank you for sharing it. There are more like it in the following links:
http://www.fractalforums.com/new-theories-and-research/extending-the-definition-of-a-burning-ship
http://www.fractalforums.com/animations-showcase-(rate-my-short-animation)/infinite-burning-ships-rotating-the-folding-axis/
I very much want to revisit those fractals. Some of the most beautiful 2D fractal shapes I've ever seen are deep in those twisted fractals. If you can read and understand my incoherent posts about them, you can recreate them and explore that frontier yourself
Code: [Select]
#include <complex>#include <iostream>using namespace std;int main(){for(int y=0;++y<22;){for(intx=0;++x<60;){complex<float>z,c={3*(float)(x)/60-2,2.5// wes*(float)(y)/22-1.25};int i=0;while(abs(z)<2&&++i<12)z=pow(z,2)+c;cout<<(i<12?'.':'*');}cout<<'\n';}cout<<endl;}// 2017