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Quads and tails

The all-important file quads+tails.txt provides an essential basis for exploring the octomino network described in the article "Self-Tiling Tile Sets". It lists those 4,512 computer-discovered quads (sets of 4 distinct octominoes) that are able to tile at least 4 distinct bigocto's (doubled-in-size-octominoes). The quads are listed in lexical order, a feature that greatly facilitates searches. The file is available here.  


The file contains 4,512 rows of integers. In each, following the row number at extreme left, the subsequent 4 numbers are piece codes that identify the four octominoes making up the quad. The corresponding octomino shapes can be found by clicking on 'The 61 Octominoes' (61, because it turns out that just 61 different octominoes are involved in the network). An arrow separates the four quad numbers from the remainder or 'tail' of the row which consists of the piece codes of those bigocto's that can be tiled by the quad. Thus, when a piece code appears in a quad it represents an octomino; when it appears in a tail it represents a bigocto. Since quads that tile less than 4 bigocto's are of no interest, the number of bigocto's listed is always 4 or more. In some cases very much more. The longest, row 928, contains 161 bigocto codes.

For a closely related file click on Quads tiling quads.


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