POLYOMINO_MULTIHEDRAL_MATRIX
Linear System for Polyomino Multihedral Tiling

POLYOMINO_MULTIHEDRAL_MATRIX, a MATLAB library which is given matrices defining a region R and a set of several polyominoes P, and returns the linear system A*x=b that must be solved for binary solutions x, that represent possible tilings of the region R by the polyominoes in P.

A region R is a subset of an MRxNR grid of squares.

A polyomino P(k) is a subset of an MRxNR grid of squares.

Both objects are represented by binary matrices.

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_matrix is available in a MATLAB version.

Related Data and Programs:

polyomino_multihedral_matrix_test

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_embed_list.m, for each possible embedding, lists the translation necessary to to apply to the polyomino.
• polyomino_embed_number.m, reports the number of ways a polyomino can be embedded in a region.
• polyomino_index.m, computes an index for each nonzero polyomino entry.
• polyomino_multihedral_matrix.m, determines the matrix and right hand side for a polyomino multihedral problem.
• polyomino_multihedral_variants.m, carries out reflections and rotations of a set of polyominoes to determine which transformations yield distinct variants.
• polyomino_print.m, prints a polyomino.
• polyomino_transform.m, carries out reflections and rotations of a polyomino.
• timestamp.m, prints the YMDHMS date as a timestamp.