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Rock Paper Squiggles

We’ve seen non-transitive dice, and we’ve had cellular automata coming out of our ears (and proceeding deterministically). Now, this:

A post by the CA’s creator describes in more detail what’s going on, although essentially the idea is that red, green and blue are able to destroy each other in a similar way to rock-paper-scissors, and the result of letting them play for a while is quite interesting. My favourite YouTube comment here has got to be the amazing and prescient “I’m high and what is this?”

Möbius house

Mobius HouseSince the Möbius band is such a cool object, it follows that anything made from a Möbius band or in the shape of a Möbius band is therefore also supercool. Also: the bigger, the better. So how about a Möbius house?

Korean architects Planning Korea have come up with a scale model and computer generated images of an amazing house based on the one-sided wonder, which uses the face of the Möbius strip as the roof and walls, with the front and back of the house covered in glass windows. It would take twice as long to paint the outside of your house (it’s also the inside), but otherwise you’d be sitting pretty. I do hope that’s a Möbius shed visible in the background, and a probability tree in the garden.

If you’re looking for something to sit on in your non-orientable domicile – presumably, while wearing your Conjoined Möbius Hat – there’s always this chair, which was incorrectly identified as being a Möbius strip by NotCot, and features a distinctly Möbiusy-looking wooden frame with coloured hanging net, to throw yourself into at the end of a long day of one-sided arguments and twisted stripping (don’t ask).

Via Alex Bellos on Twitter.

3D-printed mathematical objects roundup

3D printers are ace. People are using them to make all sorts of cool things. If you can describe a shape to a computer, it’s very easy to send that description to a 3D printer, which will happily smoosh some substrates together to make a real model of your shape. Mathematicians are able to describe all sorts of crazy shapes, in exactly the amount of detail computers need, so they’ve taken to 3D printing like ducks to water.

Thingiverse is just a repository for designs, so if you see something you like you’ll have to find your own 3D printer. Shapeways makes the objects and posts them to you; prices can vary from just a few euros to hundreds, depending on the size of the object and the materials used.

As with all other kinds of mathematical art, there’s a huge amount of repetition of the same few ideas, but also a few really interesting and unique designs. I’ve picked a couple of representatives from each of the popular topics, but do search around if you want a version with slightly different parameters; you’re bound to find something suitable.

For the past few months I’ve been quietly compiling a list of interesting mathematical objects I’ve found on the main 3D printing catalogues, Thingiverse and Shapeways. With Christmas approaching, I thought now would be as good a time as any to share what I’ve found.