File talk:All 369 free octominoes.svg

Fixed problem -- I hope

The following correct dispute was made concerning this diagram:

There are five duplicates and two heptominoes:

1. 7th row / 15th column = 7 units
2. 17th row / 12th column = 7 units
3. 5th row / 10th column => 5th row / 18th column
4. 9th row / 1st column => 9th row / 4th column
5. 11th row / 12th column => 11th row / 15th column
6. 11th row / 1st column => 11th row / 8th column
7. 14th row / 17th column => 14th row / 19th column

There are also 7 unrepresented pieces.

I made the indicated changes and moved the disputed-diagram template to this page. Hopefully I made the changes correctly and didn't introduce any new problems. Please let me know if I did. -- Nonenmac (talk) 19:34, 22 November 2009 (UTC)

There are still some problems:

• 7th row/14th column: still a heptomino, but 7th row/16th column is a nonomino now
• 17th row/9th column: should probably be blue (C₂ symmetry)

--ἀνυπόδητος (talk) 13:22, 24 November 2009 (UTC)

I made the above changes. Thanks for letting me know. -- Nonenmac (talk) 15:18, 28 November 2009 (UTC)

Comments imported from my Commons talk page concerning this diagram

Hi, my research group has been doing some work on polyominos and there are two heptominos in your octomino figure. The first is 6 from the right on line 7. The second is the second green structure on line 17. I removed the figure from the polyomino and octomino pages but it'd be good to fix - is there a bug in your enumeration algorithm? The integer sequence A000105 suggests that there are 369 octominos - if this number is from your algorithm, it should be fixed.

See #Octomino_Image_Error. Splarka (talk) 22:36, 17 November 2009 (UTC)

I made the changes that you indicated in the octomino diagram. You may want to check to make sure that I didn't introduce any new problems. I moved the disputed-diagram template in the image's talk page. You can move it back if there's a problem. -- Nonenmac (talk) 23:13, 22 November 2009 (UTC)

It was too much work to check manually once! Might be better for you to check by generating then with a different method and comparing results? I am not sure how you have them organized. Ishino Keiichiro's polyomino data is apparently organized from most significant to least significant bit, in an 8x4 grid for octominoes. So you get: this (and the binary representation). In a chart it would look like testwiki:File:369.svg.

This could probably be easily recreated by taking all permutations of 8 bits in a 32 bit number, organizing in the 8x4 grid, checking and eliminating diagonals/floaters, rotating/mirroring/upper-lefting all to most significant bits and removing duplicates, and then sorting by most significant bits (lazily done by converting to binary numbers and sorting). Just an idea. Splarka (talk) 00:28, 23 November 2009 (UTC)

Comments imported from my Wikipedia talk page concerning this diagram

Just in case you haven't been watching your talk page on the Commons, someone found errors in your Heptomino and Octomino images. I've identified how the heptomino image should be corrected, see Wikipedia talk:WikiProject Mathematics for details. I would make the correction myself, but the file uses some sophisticated SVG features that the editor I'm using, Inkscape, doesn't handle very well.--RDBury (talk) 02:58, 27 October 2009 (UTC)

I made the changes that were indicated in the octomino diagram. You may want to check to make sure that I didn't introduce any new problems. I moved the disputed-diagram template in the image's talk page. You can move it back if there's a problem. -- Nonenmac (talk) 23:18, 22 November 2009 (UTC)

Thanks for taking the trouble! However, there still seem to be two problems:

• 7th row/14th column: still a heptomino, but 7th row/16th column is a nonomino now
• 17th row/9th column: should probably be blue (C₂ symmetry)

Cheers --ἀνυπόδητος (talk) 15:52, 23 November 2009 (UTC)

Mathworld has an octomino image to compare to but it can't be used directly as it's under copyright (not to mention Mathworld occasionally has errors). It could be used for verification purposes though.--RDBury (talk) 21:28, 23 November 2009 (UTC)

The Image still has an error in it; row 16, column 2 is the same as row 18, last column. I'm deleting the image from the article for now. Still trying to work out which one is missing.--RDBury (talk) 15:21, 29 November 2009 (UTC)

FYI, the missing octomino is

    X
X   X X
X X X 
    X

--RDBury (talk) 20:23, 30 November 2009 (UTC)

Thanks. I changed the last octomino in the next-to-last row to the one you diagrammed above. -- Nonenmac (talk) 23:20, 3 December 2009 (UTC)

Two more issues:

• The last-but-one octomino should be purple, not green, to match the colour coding of the heptominoes (2 reflection symmetries along the diagonals).
• What about the C₄ octomino (also in the last row)? Wouldn't be blue more appropriate, or a different colour altogether?

Cheers, ἀνυπόδητος (talk) 15:44, 3 December 2009 (UTC)

You are right. I changed the next-to-last octomino from green to purple, and the made C₄ octomino yellow since it is unique. -- Nonenmac (talk) 23:20, 3 December 2009 (UTC)

I just glanced up at the diagram and noticed that the square bagel-looking octomino at row-9, col-6 is also a C₄ figure and maybe should be made yellow too. Though it does fit blue category definition. -- Nonenmac (talk) 23:25, 3 December 2009 (UTC)

The bagel has D₄ symmetry. I think purple is fine because it combines the symmetries of the other purple octominoes (reflection symmetry along the gridlines plus reflection symmetry along the diagonals). Unless you want to split this subset into three, but then the heptomino files (File:Heptominoes.svg, File:Rotation and Reflection Symmetrical Heptominoes.svg) would have to be changed as well: The last one in File:Rotation and Reflection Symmetrical Heptominoes.svg also has two diagonal reflection symmetries. But this probably would be overdoing it a bit. --ἀνυπόδητος (talk) 11:49, 4 December 2009 (UTC)

Symmetry tables for reference

Heptominoes

90° reflection

45° reflection

Rotation

Both

Octominoes

90° reflection

45° reflection

Rotation (C2)

Rotation (C4)

Both