pentominoes

pentominoes, a MATLAB library which provides some utilities for manipulating pentominoes.

A pentomino is a shape formed by connecting 5 unit squares edgewise. Ignoring reflection and rotation, there are 12 distinct pentominoes, nicknamed F, I, L, N, P, T, U, V, W, X, Y and Z.

A classical problem in combinatorics is the "tiling problem", which asks whether a given region can be constructed by using each pentomino once, or by using a single pentomino multiple times, or with other restrictions on the components.

The pentominoes are special cases of the general class of "polyominoes", which a formed by connecting any number of unit squares.

Licensing:

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

Languages:

pentominoes is available in a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

pentominoes_test

Source Code:

• cell_ij_fill.m fills a unit square with a color.
• pentomino_display.m displays a particular pentomino in a 5x5 grid.
• pentomino_matrix.m returns a 0/1 matrix defining a particular pentomino.
• pentomino_name.m given an index between 1 and 12, returns the corresponding name F, I, L, N, P, T, U, V, W, X, Y, or Z.
• pentomino_pack.m packs the pentominoes into an MxNx12 array.
• pentomino_print.m, prints a pentomino.