Algorithmic Mathematical Art (2004)

Here is another interesting technique for generating algorithmic art, from Renato Budinich: 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).

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

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

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, 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. 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".

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

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.

No L-systems? Aw...

http://algorithmicbotany.org/papers/

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

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-...

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/

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

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?