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Tie, tie, tie a tie / Fly, fly, fly as you might

knot tie

Novel knot news now! You might already be aware that there are 85 ways to tie a tie. Well, cast that preconception aside because there are actually loads.

Ghost Diagrams

ghost diagram

Yet another fun toy for you. Give a computer a set of tiles defined by what their edges look like, can you fit them together? That problem is undecidable, since you can encode Turing machines as sets of tiles, but it turns out it’s fun to watch a computer try.

Ghost Diagrams asks you for a set of tiles (or it’ll make some up if you didn’t bring one) and shows you its attempts to make them fit together. It’s very pretty, and quite mesmerising. Sometimes it looks even better when you turn on the “knotwork” option.

Paul Harrison created Ghost Diagrams while writing his PhD thesis, Image Texture Tools: Texture Synthesis, Texture Transfer, and Plausible Restoration. He’s written a short blog post about the program.

Here are a few patterns I liked: 1, 2, 3, 4, 5.

via John Baez on Google+.

Tying knots in light

According to this post on, which reports on this paper in science journal Nature, there’s some beautiful physics which results from tying knots in light. It opens, “New research published today seeks to push the discovery that light can be tied in knots to the next level.” Between us, I wasn’t actually aware of the discovery that light can be tied in knots (and I’ve done a fair amount of knot theory, and observed a decent quantity of light) – but apparently it’s something scientists have been exploring for years.

A spinning optical soliton (wave pulse) can spontaneously create knotted and linked structures, as the soliton curves around in space, and while previously it’s been observed after engineering them to happen, now the knots are forming spontaneously, like ” those annoying knots that you always get in electrical cables.” (see: here). The paper suggests similar behaviour might be seen in other types of wavefronts, such as superfluids and trapped matter waves. For anyone who got lost around ‘soliton’, rest assured it involves the use of lasers. Obviously.

More information

Beautiful physics: tying knots in light on

Spontaneous knotting of self-trapped waves in Nature

via @haggismaths (retweeting @eusci) on Twitter.