SCRIPTS
Set up and plot polyomino tiling problems

SCRIPTS is a small collection of MATLAB scripts which set up sample polyomino tiling problems; once a solution is obtained with an external integer linear programming package, scripts are available to simplify the process of displaying the solution.

Before running an example, it is assumed that all the necessary MATLAB codes have been copied from this directory. Then one can

1. Run the appropriate 'LPmake' file in MATLAB;
2. Pass the resulting lp file to an appropriate optimizing package, requesting a solution;
3. Run the appropriate MATLAB plotting script, plot_mono() or plot_multi(), specifying the appropriate input;
4. Wait for all the image files to be generated.

Licensing:

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

Reference:

1. M R Garvie, John Burkardt,
   A mathematical model for tiling finite regions of the plane with polyominoes,
   To appear, 2018.

Scripts that set up example problems:

• LPmake_Figure8a.m, defines some arrays needed to solve the example displayed in Figure 8a using 30 copies of the L-triomino to tile the 18 x 5 rectangle (you can use plot_mono() afterwards);
• LPmake_Figure8b.m, defines some arrays needed to solve the example displayed in Figure 8b using 12 pentominoes to tile the 6 x 10 rectangle (you can use plot_multi() afterwards);
• LPmake_Figure9a.m, defines some arrays needed to solve the example displayed in Figure 9a using 4 copies each of 8 octominoes to tile a 16 x 24 region with an 8 x 16 notch (you can use plot_multi() afterwards);
• LPmake_Figure9b.m, defines some arrays needed to solve the example displayed in Figure 9b using 12 pentominoes (with copies) to tile the 11 x 11 square with four 2 x 2 holes (you can use plot_multi() afterwards);
• LPmake_Figure10.m, defines some arrays needed to solve the example displayed in Figure 10 using 600 copies of a single hexomino to tile a 60 x 60 square (you can use plot_mono() afterwards);
• LPmake_Figure11.m, defines some arrays needed to solve the example displayed in Figure 11 using 20 copies of each of the 12 pentominoes to tile a 30 x 40 region (you can use plot_multi() afterwards);

Scripts that plot solutions.

• plot_mono.m, plots monohedral tilings after optimization;
• plot_multi.m, plots multihedral tilings after optimization;