TatamiMaker: A Combinatorially Rich Mechanical Game Board
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Transcript of TatamiMaker: A Combinatorially Rich Mechanical Game Board
Tatami Maker: A CombinatoriallyRich Mechanical Game Board
Alejandro Erickson
University of VictoriaBridges 2013, Enschede, the Netherlands
July 27-31, 2013
Japanese Tatami matsTraditional Japanese floor mats made of soft wovenstraw.
A 17th Century layout rule:No four mats may meet.
Let’s play a gameTatami restrictionNo four tiles meet (e.g. at grid intersections).
Tatami-cover the 4 × 5 grid with dominoes, and, and monominoes, . Add or remove a tile.
Mathematical history
No four dominoes (mats) may meetTatami coverings of rectangles were considered byMitsuyoshi Yoshida, and Don Knuth (about 370years later).
Tatami researchI Ruskey, Woodcock, 2009, Counting
fixed-height tatami tilings.
I Alhazov, Morita, Iwamoto, 2010, A Note onTatami Tilings.
I E, Ruskey, Schurch, Woodcock, 2011,Monomer-Dimer Tatami Tilings of RectangularRegions.
I E, Schurch, 2012, Monomer-dimer tatamitilings of square regions.
I E, Ruskey, 2013, Domino Tatami Covering isNP-complete.
I E, Ruskey, 2013, Enumerating maximal tatamimat coverings of square grids with v verticaldominoes.
Tatami researchI Ruskey, Woodcock, 2009, Counting
fixed-height tatami tilings.I Alhazov, Morita, Iwamoto, 2010, A Note on
Tatami Tilings.
I E, Ruskey, Schurch, Woodcock, 2011,Monomer-Dimer Tatami Tilings of RectangularRegions.
I E, Schurch, 2012, Monomer-dimer tatamitilings of square regions.
I E, Ruskey, 2013, Domino Tatami Covering isNP-complete.
I E, Ruskey, 2013, Enumerating maximal tatamimat coverings of square grids with v verticaldominoes.
Tatami researchI Ruskey, Woodcock, 2009, Counting
fixed-height tatami tilings.I Alhazov, Morita, Iwamoto, 2010, A Note on
Tatami Tilings.I E, Ruskey, Schurch, Woodcock, 2011,
Monomer-Dimer Tatami Tilings of RectangularRegions.
I E, Schurch, 2012, Monomer-dimer tatamitilings of square regions.
I E, Ruskey, 2013, Domino Tatami Covering isNP-complete.
I E, Ruskey, 2013, Enumerating maximal tatamimat coverings of square grids with v verticaldominoes.
Tatami researchI Ruskey, Woodcock, 2009, Counting
fixed-height tatami tilings.I Alhazov, Morita, Iwamoto, 2010, A Note on
Tatami Tilings.I E, Ruskey, Schurch, Woodcock, 2011,
Monomer-Dimer Tatami Tilings of RectangularRegions.
I E, Schurch, 2012, Monomer-dimer tatamitilings of square regions.
I E, Ruskey, 2013, Domino Tatami Covering isNP-complete.
I E, Ruskey, 2013, Enumerating maximal tatamimat coverings of square grids with v verticaldominoes.
Tatami researchI Ruskey, Woodcock, 2009, Counting
fixed-height tatami tilings.I Alhazov, Morita, Iwamoto, 2010, A Note on
Tatami Tilings.I E, Ruskey, Schurch, Woodcock, 2011,
Monomer-Dimer Tatami Tilings of RectangularRegions.
I E, Schurch, 2012, Monomer-dimer tatamitilings of square regions.
I E, Ruskey, 2013, Domino Tatami Covering isNP-complete.
I E, Ruskey, 2013, Enumerating maximal tatamimat coverings of square grids with v verticaldominoes.
Tatami researchI Ruskey, Woodcock, 2009, Counting
fixed-height tatami tilings.I Alhazov, Morita, Iwamoto, 2010, A Note on
Tatami Tilings.I E, Ruskey, Schurch, Woodcock, 2011,
Monomer-Dimer Tatami Tilings of RectangularRegions.
I E, Schurch, 2012, Monomer-dimer tatamitilings of square regions.
I E, Ruskey, 2013, Domino Tatami Covering isNP-complete.
I E, Ruskey, 2013, Enumerating maximal tatamimat coverings of square grids with v verticaldominoes.
Tatami research
Hold your questions, there are no known applications.
Tatami research
Hold your questions, there are no known applications.
Tatami coverings are only known to be applicable togames and art
Tatami research
Hold your questions, there are no known applications.
Tatami coverings areonly known to be applicable to games
and art!!!
Tomoku!
Pen-and-paper falls short
I Solution is not aesthetically appealing.
I May require backtracking and erasing.
I Easy to forget the tatami restriction.
I Tatami Maker solves these problems.
Tomoku!
Pen-and-paper falls short
I Solution is not aesthetically appealing.
I May require backtracking and erasing.
I Easy to forget the tatami restriction.
I Tatami Maker solves these problems.
Tomoku!
Pen-and-paper falls short
I Solution is not aesthetically appealing.
I May require backtracking and erasing.
I Easy to forget the tatami restriction.
I Tatami Maker solves these problems.
Tomoku!
Pen-and-paper falls short
I Solution is not aesthetically appealing.
I May require backtracking and erasing.
I Easy to forget the tatami restriction.
I Tatami Maker solves these problems.
Tomoku!
Pen-and-paper falls short
I Solution is not aesthetically appealing.
I May require backtracking and erasing.
I Easy to forget the tatami restriction.
I Tatami Maker solves these problems.
Tomoku!
Pen-and-paper falls short
I Solution is not aesthetically appealing.
I May require backtracking and erasing.
I Easy to forget the tatami restriction.
I Tatami Maker solves these problems.
Tomoku!
Pen-and-paper falls short
I Solution is not aesthetically appealing.
I May require backtracking and erasing.
I Easy to forget the tatami restriction.
I Tatami Maker solves these problems.
Tatami Maker
Tatami Maker
Tatami Maker
Tatami Maker
Tatami Maker
Tatami Maker
Design iterations
Design iterations
Design iterations
Design iterations
Design iterations
Design iterations
Design iterations
Wish list
I Overcome the manufacturing flaws in theprototype.
I Perfect the overlays and game play.
I Patent Tatami Maker and publish a game?
Wish list
I Overcome the manufacturing flaws in theprototype.
I Perfect the overlays and game play.
I Patent Tatami Maker and publish a game?
Wish list
I Overcome the manufacturing flaws in theprototype.
I Perfect the overlays and game play.
I Patent Tatami Maker and publish a game?