From 707163ddd8df67f4691f6f105a8b067974f6a4e6 Mon Sep 17 00:00:00 2001 From: j-james Date: Fri, 4 Nov 2022 03:37:36 -0700 Subject: Partial Wang tiling --- entries/jj/tiles/README.md | 7 +++++++ entries/jj/tiles/fib.png | Bin 0 -> 26917 bytes 2 files changed, 7 insertions(+) create mode 100644 entries/jj/tiles/README.md create mode 100644 entries/jj/tiles/fib.png (limited to 'entries/jj/tiles') diff --git a/entries/jj/tiles/README.md b/entries/jj/tiles/README.md new file mode 100644 index 0000000..a7b5fd1 --- /dev/null +++ b/entries/jj/tiles/README.md @@ -0,0 +1,7 @@ +# Partial 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. + +The algorithm for this is adapted from https://grahamshawcross.com/2012/10/12/wang-tiles-and-turing-machines/ (with some fixes and optimizations). diff --git a/entries/jj/tiles/fib.png b/entries/jj/tiles/fib.png new file mode 100644 index 0000000..66e8404 Binary files /dev/null and b/entries/jj/tiles/fib.png differ -- cgit v1.2.3-70-g09d2