variomino


variomino, a MATLAB code which considers variominoes, which are polyominoes in which each square has been assigned a positive label or "variety", and the determination of tilings of a region using a specific set of variominoes.

Licensing:

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

Languages:

variomino is available in a MATLAB version.

Related Data and Programs:

variomino_test

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.

chrominoes, a MATLAB code which searches for tilings of a polygonal region using polyominoes, in which a coloring scheme is used to reduce the problem size and quickly eliminate certain arrangements.

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.

eternity_hexity, a MATLAB code which evaluates and manipulates a six-fold parity quantity associated with grids and tiles used in the Eternity puzzle.

pariomino, a MATLAB code which considers pariominoes, which are polyominoes with a checkerboard parity, and the determination of tilings of a region using a specific set of pariominoes.

polyiamonds, a MATLAB code which works with polyiamonds, simple shapes constructed by edgewise connections of congruent equilateral triangles.

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. Marcus Garvie, John Burkardt,
    A new mathematical model for tiling finite regions of the plane with polyominoes,
    Contributions to Discrete Mathematics,
    Volume 15, Number 2, July 2020.
  2. Solomon Golomb,
    Polyominoes: Puzzles, Patterns, Problems, and Packings,
    Princeton University Press, 1996,
    ISBN: 9780691024448.

Source code:


Last revised on 23 April 2023.