POLYOMINO_MONOHEDRAL_TILING_PRINT
Print Solutions of Polyomino Monohedral Tiling

POLYOMINO_MONOHEDRAL_TILING_PRINT, a MATLAB library which is given matrices defining a region R and a polyomino P, and a vector X, computed by POLYOMINO_MONOHEDRAL, which represents a tiling of R by P, and prints out a representation of that tiling.

The problem being solved is discussed in the documentation for POLYOMINO_MONOHEDRAL. Briefly, a region R is to be tiled by copies of a single polyomino P. The solution procedure treats as "variables" all distinct rotation, reflections, and translations of P that fit exactly onto some portion of R. The solution is a binary list that indicates a selection of these variables that tile R completely.

This function takes the solution vector of selected variables, such as:

  1 0 1 0 1 0 0 1 0 0

  1  1   
  8  3  3
  8  5  5

Licensing:

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

Languages:

polyomino_monohedral_tiling_print is available in a MATLAB version.

Related Data and Programs:

polyomino_monohedral_tiling_print_test

Source Code:

• 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_equal.m, is true if two polyominoes are equal.
• polyomino_index.m, computes an index for each nonzero polyomino entry.
• polyomino_monohedral_matrix.m, determines the matrix and right hand side for a polyomino monohedral problem.
• polyomino_monohedral_tiling_print.m, is given matrices defining a region R and a polyomino P, and a vector X, computed by POLYOMINO_MONOHEDRAL, which represents a tiling of R by P, and prints out a representation of that tiling.
• polyomino_monohedral_variants.m, carries out reflections and rotations of a polyomino to determine which transformations yield distinct variants.
• polyomino_transform.m, carries out reflections and rotations of a polyomino.
• timestamp.m, prints the YMDHMS date as a timestamp.