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Algorithmic Mathematical Art (2004)

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Re: Algorithmic Mathematical Art (2004)

#11

Post by tromp »

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

Re: Algorithmic Mathematical Art (2004)

#15

Post by pncnmnp »

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).

Re: Algorithmic Mathematical Art (2004)

#16

Post by begueradj »

pncnmnp wrote: post #15

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…

Interesting those PDF files (links in the bottom).

Re: Algorithmic Mathematical Art (2004)

#18

Post by sevensor »

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".

Re: Algorithmic Mathematical Art (2004)

#20

Post by Someone »

sevensor wrote: post #18

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 n…

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