8 Octominoes Tile an 8x8 Square
a MATLAB program which
sets up a problem in which an 8x8 square is to be tiled by
8 distinct octominoes.
Because this problem results in a large linear system to be solved,
we simply set up the linear system, write it to an LP file, and have
CPLEX compute all solutions. The resulting solutions are then read by
CPLEX_SOLUTION_READ, and can be printed or plotted.
Because of the symmetry of the problem, the 8 solutions that are computed
actually represent a single solution, which may be rotated and reflected
to generate 8 variations.
The computer code and data files described and made available on this web page
are distributed under
the GNU LGPL license.
polyomino_multihedral_example_octomino is available in
a MATLAB version.
Related Data and Programs:
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.
for each possible embedding, lists the translation necessary to
to apply to the polyomino.
reports the number of ways a polyomino can be embedded in a region.
computes an index for each nonzero polyomino entry.
writes an LP file describing a particular problem.
computes the linear system for the octomino example.
plots the solutions of the octomino example.
prints the solutions of the octomino example.
determines the matrix and right hand side for a polyomino multihedral
prints a tiling of a region R by a set of polyominoes P, based on a solution
computed by polyomino_multihedral.
carries out reflections and rotations of a set of polyominoes to
determine which transformations yield distinct variants.
prints a polyomino.
carries out reflections and rotations of a polyomino.
prints a set of polyominoes.
prints the current YMDHMS date as a timestamp.
Last revised on 03 March 2019