eternity_tile

eternity_tile, a MATLAB code which considers the individual tiles of the eternity puzzle, 209 distinct pieces, each formed by 36 contiguous 30-60-90 triangles, known as polydrafters, as well as tiles for the serenity and trinity puzzles, and the hat and turtle aperiodic monotiles.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

eternity_tile is available in a MATLAB version and an Octave version.

Related Data and Programs:

eternity_tile_test

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, 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.
  2. Solomon Golomb,
    Polyominoes: Puzzles, Patterns, Problems, and Packings,
    Princeton University Press, 1996,
    ISBN: 9780691024448
  3. Ed Pegg,
    Polyform Patterns,
    in Tribute to a Mathemagician,
    Barry Cipra, Erik Demaine, Martin Demaine, editors,
    pages 119-125, A K Peters, 2005.
  4. Mark Wainwright,
    Prize specimens,
    Plus magazine,
    01 January 2001,
    https://plus.maths.org/content/prize-specimens

Source code:

Last revised on 18 April 2024.