boundary_word


boundary_word, an Octave code which works with a polyomino that is described by its boundary word, a sequence of U/D/L/R symbols that indicate how to trace out its 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 some boundary word schemes, 8 symbols are required, to allow for movement in the N, S, E, W, NE, SE, NW, and SW directions.

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

Licensing:

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

Languages:

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

Related Data and Programs:

boundary_word_test

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

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

polyominoes, an Octave 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.

Source Code:


Last modified on 17 May 2021.