# boundary_word_square

boundary_word_square, a MATLAB code which describes the outline of an object on a grid of squares, using a string of symbols that represent the sequence of steps tracing out the boundary.

The symbols might be 'u', 'd', 'r', and 'l', indicating that the boundary is to be drawn by a succession of movements of unit length, that are up, down, right or left.

In image processing, boundary words are known as "chain codes".

### Languages:

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

### Related Data and Programs:

boundary_word_drafter, a MATLAB code which describes the outline of an object on a grid of drafters, or 30-60-90 triangles, using a string of symbols that represent the sequence of steps tracing out the boundary.

boundary_word_hexagon, a MATLAB code which describes the outline of an object on a grid of hexagons, using a string of symbols that represent the sequence of steps tracing out the boundary.

boundary_word_triangle, a MATLAB code which describes the outline of an object on a grid of triangles, using a string of symbols that represent the sequence of steps tracing out the boundary.

eternity, a MATLAB code which considers the eternity puzzle, which considers an irregular dodecagon shape that is to be tiled by 209 distinct pieces, each formed by 36 contiguous 30-60-90 triangles, known as polydrafters.

pariomino, a MATLAB code which considers pariominoes, which are polyominoes with a checkerboard parity.

polyomino_parity, a MATLAB code which uses parity considerations to determine whether a given set of polyominoes can tile a specified region.

polyominoes, a MATLAB code which defines, solves, and plots a variety of polyomino tiling problems, which are solved by a direct algebraic approach involving the reduced row echelon form (RREF) of a specific matrix, instead of the more typical brute-force or backtracking methods.

### Reference:

1. George Bell,
The dynamics of spinning polyominoes,
Gathering for Gardner, G4G13.
2. Srecko Briek, Gilbert Labelle, Ariane Lacasse,
Algorithms for polyominoes based on the discrete Green theorem,
Discrete Applied Mathematics,
Volume 147, pages 187-205, 2005.