POLYOMINO_MULTIHEDRAL_VARIANTS
Compute Distinct Polyomino Variants

POLYOMINO_MULTIHEDRAL_VARIANTS, a MATLAB program which computes the distinct variants of one or more polyominoes under reflection and 90 degree rotations.

A polyomino P is a shape formed by connecting unit squares. It can be described by a rectangular binary matrix. The matrix is assumed to be "top-left tight", that is, there must be a 1 in the first row, and in the first column of the matrix, but there may be trailing rows and columns of zeroes.

A polyomino can be rotated by 90, 180, or 270 degrees, and it can be reflected. There are 8 combinations of these transformations possible, so there are 8 variations of a given polyomino. However, because of symmetry, there may be 1, 2, 4, or 8 distinct variations.

This program accepts the binary matrices describing one or more polyominoes, generates all the possible variations, and returns those which are distinct.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Source Code:

• polyomino_condense.m, cleans up a matrix that represents a polyomino by setting all nonzero entries to 1, and removing initial and final rows and columns of zeros.
• polyomino_multihedral_variants.m, carries out reflections and rotations of a polyomino to determine which transformations yield distinct variants.
• polyomino_print.m, prints a polyomino.
• polyomino_transform.m, carries out reflections and rotations of a polyomino.
• polyominoes_print.m, prints polyominoes stored in an array.
• timestamp.m, prints the YMDHMS date as a timestamp.

Examples and Tests:

• polyomino_multihedral_variants_test.m
• polyomino_multihedral_variants_test.txt
• pentomino_matrix.m returns a 0/1 matrix defining a particular pentomino.