![]() | 1 | initial version |
Sage has a built-in class of polyominos, with some solving and plotting functions.
Here is an example.
Some preliminary imports.
sage: import itertools
sage: from sage.combinat.tiling import TilingSolver, Polyomino
Define a polyomino and a chessboard.
sage: domino = Polyomino([(0, 0), (1, 0)], color='steelblue')
sage: s = set(itertools.product(range(6), repeat=2))
sage: s.difference_update([(3, 3), (3, 4), (4, 3), (4, 4)])
sage: chessboard = Polyomino(s)
Define the tiling problem.
sage: T = TilingSolver([domino], box=chessboard, reflection=False, rotation=True, reusable=True)
Count solutions.
sage: T.number_of_solutions()
Store the solutions in a list.
sage: solutions = list(T.solve())
Turn two of the solutions into graphic objects.
sage: G = sum([piece.show2d() for piece in solutions[0]], Graphics())
sage: GG = sum([piece.show2d() for piece in solutions[220]], Graphics())
Save them to file, or view them.
sage: graphics_array([G, GG]).save("domino-tilings.png", aspect_ratio=1, axes=False)
sage: graphics_array([G, GG]).show(aspect_ratio=1, axes=False, figsize=5)
![]() | 2 | No.2 Revision |
Sage has a built-in class of polyominos, with some solving and plotting functions.
Here is an example.
Some preliminary imports.
sage: import itertools
sage: from sage.combinat.tiling import TilingSolver, Polyomino
Define a polyomino and a chessboard.
sage: domino = Polyomino([(0, 0), (1, 0)], color='steelblue')
sage: s = set(itertools.product(range(6), repeat=2))
sage: s.difference_update([(3, 3), (3, 4), (4, 3), (4, 4)])
sage: chessboard = Polyomino(s)
Define the tiling problem.
sage: T = TilingSolver([domino], box=chessboard, reflection=False, rotation=True, reusable=True)
Count solutions.
sage: T.number_of_solutions()
Store the solutions in a list.
sage: solutions = list(T.solve())
Turn two of the solutions into graphic objects.
sage: G = sum([piece.show2d() for piece in solutions[0]], Graphics())
sage: GG = sum([piece.show2d() for piece in solutions[220]], Graphics())
Save them to file, or view them.
sage: graphics_array([G, GG]).save("domino-tilings.png", aspect_ratio=1, axes=False)
sage: graphics_array([G, GG]).show(aspect_ratio=1, axes=False, figsize=5)