eternity2


eternity2, a MATLAB code which considers the eternity II puzzle, which considers a 16x16 array of unit squares inside a frame, to be covered by 256 square tiles, with colored edges. Adjacent tiles must have matching edge colors.

Licensing:

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

Languages:

eternity2 is available in a MATLAB version.

Related Data and Programs:

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.

eternity2_test

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 considers polyiamonds, simple connected shapes constructed from equilateral triangles connected edgewise.

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.

trinity, a MATLAB code which considers the trinity puzzle, a smaller version of the eternity puzzle. The trinity puzzle specifies a region R composed of 144 30-60-90 triangles, and a set of 4 "tiles", T1, T2, T3 and T4, each consisting of 36 30-60-90 triangles, and seeks an arrangement of the four tiles that exactly covers the region.

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.

Source code:


Last revised on 19 February 2021.