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.

Languages:

polyomino_multihedral_variants is available in a MATLAB version.

Related Data and Programs:

polyomino_multihedral_variants_test

Source Code:


Last revised on 06 March 2019.