Post without words #21

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About Brent

Assistant Professor of Computer Science at Hendrix College. Functional programmer, mathematician, teacher, pianist, follower of Jesus.
This entry was posted in combinatorics, geometry, posts without words and tagged , , . Bookmark the permalink.

15 Responses to Post without words #21

  1. David Eppstein says:

    OEIS knows the answer…

  2. kaligule says:

    Walking along the paths counterclockwise there is an constant number of right turns in each group of diagrams, increasing from group to group.

  3. Denis says:

    Took me a couple of looks but since the area and perimeter weren’t constant, there was a clear metric to check next. This would be an interesting challenge to automate, with removal of reflections and rotations and length variations and collision avoidance.

    • Brent says:

      “This would be an interesting challenge to automate” — that’s a very perceptive comment. In fact, the image you see above *was* generated in an automated way, and indeed, it was quite interesting! In a sense, I have been trying (off and on) to figure out how to generate this image for more than a year. I’ll explain more in future posts.

    • Ajm says:

      Consider a regular 2n+2 gon with n-1 painted edges where n=1,2,3,4….
      .
      The various such painted polygons are represented by your shapes.

  4. Naren Sundar says:

    It’s just a very difficult game of Tetris 🙂

  5. Ajm says:

    Start with a square. We bite off one of the corners to get an L shape (see second image). We can aslo bite into an edge to get a C shape (see third image). The corner biting is worth 1 bite and the edge biting is worth 2 bites. For any right angled polygon, edge biting and corner biting is defined the same way. Your shapes are the sets of n-bitten squares where n=0,1,2,3,4.

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