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diff --git a/entries/jj/tiles/README.md b/entries/jj/tiles/README.md index a7b5fd1..104d69e 100644 --- a/entries/jj/tiles/README.md +++ b/entries/jj/tiles/README.md @@ -1,7 +1,9 @@ -# Partial Wang Tiling +# Wang Tiling These are Wang tiles. For more information, see https://en.wikipedia.org/wiki/Wang_tile. -Provided that the third tile (the one with the North and West edges being black, the East edge being green, and the South edge being yellow) is placed down first, there is only one arrangement of tiles such that the tiles tile the infinite quarter-plane. This arrangement forms the Fibonacci numbers. The eleventh tile (the one with the North edge being black and the West, East, and South edges being purple) will appear in Fibonacci-spaced intervals. +There is only one arrangement of these tiles that tiles the infinite plane _aperiodically_. This arrangement forms the Fibonacci sequence. -The algorithm for this is adapted from https://grahamshawcross.com/2012/10/12/wang-tiles-and-turing-machines/ (with some fixes and optimizations). +Begin by placing down the third tile (the one with the North and West edges being black, the East edge being green, and the South edge being yellow), and continue by placing tiles such that the infinite plane can continue to be filled. The eleventh tile (the one with the North edge being black and the West, East, and South edges being purple) will appear in Fibonacci-spaced intervals. + +The algorithm for this is adapted from https://grahamshawcross.com/2012/10/12/wang-tiles-and-turing-machines/ (with some fixes and tweaks). diff --git a/entries/jj/tiles/example.png b/entries/jj/tiles/example.png Binary files differnew file mode 100644 index 0000000..28b7365 --- /dev/null +++ b/entries/jj/tiles/example.png diff --git a/entries/jj/tiles/fib.png b/entries/jj/tiles/fib.png Binary files differindex 66e8404..7668696 100644 --- a/entries/jj/tiles/fib.png +++ b/entries/jj/tiles/fib.png |
