13Jan/1014

Self-Description

by Jeff

Image text: The contents of any one panel are dependent on the contents of every panel including itself. The graph of panel dependencies is complete and bidirectional, and each node has a loop. The mouseover text has two hundred and forty-two characters.

This is a comic, like the name, that describes itself.  However, as the image text explains, the contents are dependent on themselves and the other data.

The first frame is a pie chart of the black and white percentages of the whole comic strip.  If more black or white is added to any frame in the comic, the pie chart will change.

If the pie chart changes, the graph in frame 2 will change, which will cause the pie chart to change again and so on and so forth.

The third frame is an infinite loop of the comic.  If you look hard you can see the comic again and again in the last frame.

Filed under: Math Leave a comment
Comments (14) Trackbacks (0)
  1. This would of been great as a SVG

  2. “The third frame is an infinite loop of the comic. If you look hard you can see the comic again and again in the last frame.”

    … and if the pie chart and frame 2 graph changes, the third frame would change too, which would affect the pie chart and the graph all over again.

    Thinking about how he managed to do that gives me a headache

  3. That’s the purpose of self-referential “comics” – it’s all a plot of aspirin manufacturers to sell more product.

  4. The mouseover text is also self-descriptive as the “two hundred and forty-two characters” are all characters that help drive the count to 242.

  5. No headache. It’s simple algebra. x = k + ax + bx + cx, where a, b, and c are constants for each frame. Basically, the white space around the graphs has to be proportional to the ink used for text and frames.

  6. my uncle got stomach ulcers because he took a lot of Aspirin to take care of his high blood pressure.’`~

  7. I know this is a late response, but…

    Technically, the third frame is not and *cannot* be an infinite loop; if it was intended to be taken as such, then there would be an infinite amount of black ink used. Instead, the graph is made on the explicit assumption that the third panel is merely an approximation of what such a thing would look like.

    • Actually, an infinite loop would not generate infinite ink. Since each image gets infinitely smaller, the amount of ink would reach what is called a limit. That is like the argument that a ball thrown at a wall will never reach the wall, it will just get infinitely closer and closer. In reality, we know that the ball will hit the wall at a finite time depending on speed and distance.

      However, that is all irrelevant, since this is a printed image. At some point the comic within the comic, etc will reach a single pixel in size. That pixel will be either black or white, thus ending the infinite loop for our purposes.

  8. aspirin is one of the safest anti-inflammatories that you can use for lots of things`.,

  9. aspirin has been time tested to relieve minor pains and inflammation and it is cheap too :’,

  10. AND the concept behind Comic #688 is now on a xkcd T-Shirt!
    http://store.xkcd.com/xkcd/#SelfDescriptiveShirt


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