From c37b806da507a699624ec4e800522ef4a47ad7bc Mon Sep 17 00:00:00 2001 From: braxtonhall Date: Thu, 13 Jul 2023 20:26:58 +0200 Subject: Update directories --- entries/omentic/tiles/README.md | 13 +++++++++++++ entries/omentic/tiles/example.png | Bin 0 -> 94057 bytes entries/omentic/tiles/fib.png | Bin 0 -> 26282 bytes 3 files changed, 13 insertions(+) create mode 100644 entries/omentic/tiles/README.md create mode 100644 entries/omentic/tiles/example.png create mode 100644 entries/omentic/tiles/fib.png (limited to 'entries/omentic/tiles') diff --git a/entries/omentic/tiles/README.md b/entries/omentic/tiles/README.md new file mode 100644 index 0000000..ba10578 --- /dev/null +++ b/entries/omentic/tiles/README.md @@ -0,0 +1,13 @@ +# Wang Tiling + +These are Wang tiles. For more information, see https://en.wikipedia.org/wiki/Wang_tile. + +![Wang tiles](fib.png) + +There is only one arrangement of these tiles that tiles the infinite plane _aperiodically_. This arrangement forms the Fibonacci sequence. + +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 aperiodic tiling](example.png) + +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/omentic/tiles/example.png b/entries/omentic/tiles/example.png new file mode 100644 index 0000000..28b7365 Binary files /dev/null and b/entries/omentic/tiles/example.png differ diff --git a/entries/omentic/tiles/fib.png b/entries/omentic/tiles/fib.png new file mode 100644 index 0000000..7668696 Binary files /dev/null and b/entries/omentic/tiles/fib.png differ -- cgit v1.2.3-70-g09d2