5 ms·

Algorithmic Mathematical Art (2004)

Frummy 3y ago
I've been having lots of ideas for computer-aided art recently.. Maybe seeing this article is a sign to stop pondering and start tinkering
rotten 3y ago
Check out this guy's work: https://bleuje.com/animationsite/2023_1/ https://bleuje.com/animationsite/2023_1/
- nick__m 3y ago
  awesome, thank you !
- xnx 3y ago
  Very cool. Instant follow. I also like: https://www.instagram.com/davebeesbombs/ https://www.instagram.com/davebeesbombs/
- kreelman 3y ago
  Wow. Thanks.
- replwoacause 3y ago
  This is incredible, thank you for sharing
- samstokes 3y ago
  The same artist has some excellent tutorials on how to implement a lot of those effects: https://bleuje.com/tutorials/ https://bleuje.com/tutorials/
  - sph 3y ago
    I have been looking for such an in depth tutorial on generative art for ages. It's decided, tomorrow is a day off for me to explore Processing. Thanks!
- begueradj 3y ago
  Amazing. It seems he did not share any source code, though.
- r34 3y ago
  lovely
Syzygies 3y ago
I helped out on "The Right Spin" about the astronaut Michael Foale correcting an uncontrolled roll, after a resupply vessel struck Mir 23. He made calculations on his laptop using Mathematica, including an animation. I converted the animation to broadcast video, exporting the frames and processing them using Photoshop. (Animation starts at 29:53.) https://vimeo.com/185867583 https://vimeo.com/185867583 This wasn't rocket science (at least my part). I cringe now to see the pixelated effects in this "algorithmic art". Unless I'm missing the point, and this retro effect is deliberate?
tromp 3y ago
Not only the output of programs can look artistic. Source code can as well, in graphical notation [1], like this program whose output exceeds Graham's Number: ┬─┬ ┬─┬────────── └─┤ │ │ ──┬────── │ │ │ ┬─┼────── │ │ │ └─┤ ┬─┬── │ │ │ │ ┼─┼─┬ │ │ │ │ │ ├─┘ │ │ │ │ ├─┘ │ │ │ ├─┘ │ │ ├───┘ │ ├─┘ └─┘ [1] https://tromp.github.io/cl/diagrams.html https://tromp.github.io/cl/diagrams.html
set4 3y ago
i recently found some images [1] of a gyroid i did in GLSL a few years back, similar to the borg cube in the article. unfortunately i've since lost the source code, but the formula is available online. [1] https://isaac.ac/posts/2020/sdf-gyroid/ https://isaac.ac/posts/2020/sdf-gyroid/
earslap 3y ago
There is this mostly "sterile" art presented in the page (which is cool!), and there also is the demoscene which at least needs a mention.
deleted 3y ago
[deleted]
pncnmnp 3y ago
Here is another interesting technique for generating algorithmic art, from Renato Budinich: https://renatobudinich.com/create-random-images-with-randimage/ https://renatobudinich.com/create-random-images-with-randima.... It is a beautiful algorithm using a simple two-step procedure. The first step involves taking a random gray-valued mask image and applying the path-finding procedure of the Easy Path Wavelet Transform (EPWT) to it. This path-finding technique is greedy and aims to obtain a succession of vectorized pixel values with minimal variation. It does this by always picking the next point (among the available neighbors) that yields the minimum absolute value difference in pixel values. This approach helps it select regions with similar pixel values before making a jump to pixels with significantly lighter or darker regions. Once a random path of say length N is obtained, a random color map (think of one from matplotlib or seaborn) is applied, with each point k in the path mapped to the k/N point in the color map. Et voilà! A gorgeous image appears. I've been using this as cover art for my personalized radio station software (https://github.com/pncnmnp/phoenix10.1 https://github.com/pncnmnp/phoenix10.1).
- begueradj 3y ago
  Interesting those PDF files (links in the bottom).
sevensor 3y ago
A long time ago, I wrote IrisGL code for the mathematician George Francis, who made mathematical visualization his life's work. He published this book: https://en.wikipedia.org/wiki/A_Topological_Picturebook https://en.wikipedia.org/wiki/A_Topological_Picturebook, which is worth a look, and he was forever sketching Reimann manifolds on scraps of paper with a fountain pen. Which is quite a trick. I kick myself for not hanging onto one. He maintains what for me is a very nostalgic old-internet webpage at https://new.math.uiuc.edu https://new.math.uiuc.edu. There are links at the bottom to web versions of his computer animations. Edit: If you do click on the animations, make sure to try the different commands like "morph" and "skin".
- Someone 3y ago
  That book can be borrowed from the Internet Archive: https://archive.org/details/topologicalpictu0000fran https://archive.org/details/topologicalpictu0000fran
ykonstant 3y ago
That's a lovely collection; let me add a humble illustration of Lambert's W Riemann Surface that I fried my laptop to generate: https://drive.google.com/file/d/1H6rSZ6-jx-8rqLXowzevJ1e3FD-ppJSa/view?usp=drive_link https://drive.google.com/file/d/1H6rSZ6-jx-8rqLXowzevJ1e3FD-...
YeGoblynQueenne 3y ago
No L-systems? Aw... http://algorithmicbotany.org/papers/ http://algorithmicbotany.org/papers/
gravescale 3y ago
I'm always sad when I visit Jared Tarbell's sites (http://levitated.net http://levitated.net and http://complexification.net http://complexification.net) and the applets no longer work. They were really formative in my early and mid explorations of the internet.
- tithe 3y ago
  Same here. The "Masters of Flash" were what initially got me into programming and eventually computer science.

I've been having lots of ideas for computer-aided art recently.. Maybe seeing this article is a sign to stop pondering and start tinkering

rotten 3y ago

Check out this guy's work: https://bleuje.com/animationsite/2023_1/ https://bleuje.com/animationsite/2023_1/

nick__m 3y ago
awesome, thank you !
xnx 3y ago
Very cool. Instant follow. I also like: https://www.instagram.com/davebeesbombs/ https://www.instagram.com/davebeesbombs/
kreelman 3y ago
Wow. Thanks.
replwoacause 3y ago
This is incredible, thank you for sharing
samstokes 3y ago
The same artist has some excellent tutorials on how to implement a lot of those effects: https://bleuje.com/tutorials/ https://bleuje.com/tutorials/
- sph 3y ago
  I have been looking for such an in depth tutorial on generative art for ages. It's decided, tomorrow is a day off for me to explore Processing. Thanks!
begueradj 3y ago
Amazing. It seems he did not share any source code, though.
r34 3y ago
lovely

Syzygies 3y ago

I helped out on "The Right Spin" about the astronaut Michael Foale correcting an uncontrolled roll, after a resupply vessel struck Mir 23. He made calculations on his laptop using Mathematica, including an animation. I converted the animation to broadcast video, exporting the frames and processing them using Photoshop. (Animation starts at 29:53.) https://vimeo.com/185867583 https://vimeo.com/185867583 This wasn't rocket science (at least my part). I cringe now to see the pixelated effects in this "algorithmic art". Unless I'm missing the point, and this retro effect is deliberate?

tromp 3y ago

Not only the output of programs can look artistic. Source code can as well, in graphical notation [1], like this program whose output exceeds Graham's Number: ┬─┬ ┬─┬────────── └─┤ │ │ ──┬────── │ │ │ ┬─┼────── │ │ │ └─┤ ┬─┬── │ │ │ │ ┼─┼─┬ │ │ │ │ │ ├─┘ │ │ │ │ ├─┘ │ │ │ ├─┘ │ │ ├───┘ │ ├─┘ └─┘ [1] https://tromp.github.io/cl/diagrams.html https://tromp.github.io/cl/diagrams.html

set4 3y ago

i recently found some images [1] of a gyroid i did in GLSL a few years back, similar to the borg cube in the article. unfortunately i've since lost the source code, but the formula is available online. [1] https://isaac.ac/posts/2020/sdf-gyroid/ https://isaac.ac/posts/2020/sdf-gyroid/

earslap 3y ago

There is this mostly "sterile" art presented in the page (which is cool!), and there also is the demoscene which at least needs a mention.

deleted 3y ago

[deleted]

pncnmnp 3y ago

Here is another interesting technique for generating algorithmic art, from Renato Budinich: https://renatobudinich.com/create-random-images-with-randimage/ https://renatobudinich.com/create-random-images-with-randima.... It is a beautiful algorithm using a simple two-step procedure. The first step involves taking a random gray-valued mask image and applying the path-finding procedure of the Easy Path Wavelet Transform (EPWT) to it. This path-finding technique is greedy and aims to obtain a succession of vectorized pixel values with minimal variation. It does this by always picking the next point (among the available neighbors) that yields the minimum absolute value difference in pixel values. This approach helps it select regions with similar pixel values before making a jump to pixels with significantly lighter or darker regions. Once a random path of say length N is obtained, a random color map (think of one from matplotlib or seaborn) is applied, with each point k in the path mapped to the k/N point in the color map. Et voilà! A gorgeous image appears. I've been using this as cover art for my personalized radio station software (https://github.com/pncnmnp/phoenix10.1 https://github.com/pncnmnp/phoenix10.1).

begueradj 3y ago
Interesting those PDF files (links in the bottom).

sevensor 3y ago

A long time ago, I wrote IrisGL code for the mathematician George Francis, who made mathematical visualization his life's work. He published this book: https://en.wikipedia.org/wiki/A_Topological_Picturebook https://en.wikipedia.org/wiki/A_Topological_Picturebook, which is worth a look, and he was forever sketching Reimann manifolds on scraps of paper with a fountain pen. Which is quite a trick. I kick myself for not hanging onto one. He maintains what for me is a very nostalgic old-internet webpage at https://new.math.uiuc.edu https://new.math.uiuc.edu. There are links at the bottom to web versions of his computer animations. Edit: If you do click on the animations, make sure to try the different commands like "morph" and "skin".

Someone 3y ago
That book can be borrowed from the Internet Archive: https://archive.org/details/topologicalpictu0000fran https://archive.org/details/topologicalpictu0000fran

ykonstant 3y ago

That's a lovely collection; let me add a humble illustration of Lambert's W Riemann Surface that I fried my laptop to generate: https://drive.google.com/file/d/1H6rSZ6-jx-8rqLXowzevJ1e3FD-ppJSa/view?usp=drive_link https://drive.google.com/file/d/1H6rSZ6-jx-8rqLXowzevJ1e3FD-...

YeGoblynQueenne 3y ago

No L-systems? Aw... http://algorithmicbotany.org/papers/ http://algorithmicbotany.org/papers/

gravescale 3y ago

I'm always sad when I visit Jared Tarbell's sites (http://levitated.net http://levitated.net and http://complexification.net http://complexification.net) and the applets no longer work. They were really formative in my early and mid explorations of the internet.

tithe 3y ago
Same here. The "Masters of Flash" were what initially got me into programming and eventually computer science.