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Random Domino Tilings

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size of m×n rectangle, m ≤ n
m
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
n
20
another tiling
There are 1269984011256235806017323563676759532051128909824 tilings.
Consider an
m×n
rectangle and rectangular tiles of size 1×2 (dominoes). A domino tiling of the rectangle is a placement of dominoes that covers the rectangle completely without overlaps. A tiling exists if and only if
m
and
n
are not both odd, implying
mn
is even. One tiling can readily be found: suppose
m
is even, place
m/2
dominoes vertically in the first column and repeat for the next
n
columns. This Demonstration generates random tilings of rectangles of chosen sizes and computes the total number of tilings possible.
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