6 ms·
A puzzle that tiles infinitely across both sides, based on the Klein Bottle
- dwighttk 8y ago(2016)
- baldeagle 8y agoOk, that is one of the best math + lasercutter = art links that I have seen in a while. And the concept of being able to keep moving the puzzle pieces around is pretty cool. There is also a link to upload your own art work and create your own puzzle, which is what I will be doing for this mother's day. Overall, a pretty cool link.
- oceanghost 8y agoThe soundtrack appears to be these NASA space recordings that were released in the 80s. They translated probe data into audible frequencies and released them as a CD box set.
- werdnapk 8y agoA puzzle like this will drive someone with serious OCD nuts. :)
- tempodox 8y agoThis would be even more awesome if the puzzle pieces were curved, so they'd form a Klein bottle when put together.
- mcherm 8y agoThat would be INCREDIBLY awesome, considering that it would require pieces that have a curve in to the 4th dimension (or perhaps just pieces that could pass through each other). A Klein bottle is a 2-dimensional surface cannot be embedded in a 3-dimensional space without crossing.
- tempodox 8y agoWhile this is true mathematically, there is at least one project that emulates Klein bottles in 3D quite credibly: http://www.kleinbottle.com http://www.kleinbottle.com Edit: You can even put in some liquid (the “hose” continues through the crossing). The fun part is getting it out again :)
- mcherm 8y agoThere are lots of projects that do this (implement a Klein bottle with a crossing).
- dancek 8y agoEven my dad has knit several Klein bottle hats for fun, inspired by one of those projects. I got one as a Christmas present.
- emmelaich 8y agoHey that's the famous Clifford Stoll of Cuckoo's Egg fame. Glad he is not famous only for that book. As fine as it is.
- askvictor 8y agoI have a 3D jigsaw puzzle that makes a globe (i.e. the Earth) that consists of curved plastic pieces. It shouldn't be too hard to make such a Klein puzzle, though solving it is harder. The globe puzzle includes a small bowl (of the same radius as the finished globe) to assist putting the pieces together; this wouldn't be possible with a klein bottle due to there not being a consistent radius.
- p1mrx 8y agoI think the flat version is a more authentic representation of the 4-dimensional object. If you were a 2D creature embedded in the surface of a Klein bottle, space would seem flat in every direction... at least until you went out for a walk and found the mirror-image of your house.
- deleted 8y ago[deleted]
- Semirhage 8y agoThe coolest part is if you put a few them together you open a non-orientable wormhole and pass into an Alice Universe.
- phinnaeus 8y agoI've played with one of these puzzles in person. They're incredibly cool but pretty difficult. I worked for 20 minutes and was able to tesselate a single piece into a different position. I might just be bad at it though. On the other hand, the challenge is part of the appeal to me.
- gnarbarian 8y agothis is awesome and reminds me of the tiling puzzle from the book Anathem: http://anathem.wikia.com/wiki/Teglon http://anathem.wikia.com/wiki/Teglon or https://en.wikipedia.org/wiki/Penrose_tiling https://en.wikipedia.org/wiki/Penrose_tiling I would love to have a Penrose tiling puzzle set.
- AKrumbach 8y agoI'm at work right now, but give me a day and I will design that.
- gnarbarian 8y agoWoah, Thanks! Does the AK in your name stand for Alaska? If so, I'm in Anchorage.
- AKrumbach 8y agoNo, that's my first initial and last name (A Krumbach). Anyway, "puzzle" is now available at https://drive.google.com/file/d/1KYDTZ2AVWQfWCSACUvfl5gAIHzAWXG7m/view?usp=sharing https://drive.google.com/file/d/1KYDTZ2AVWQfWCSACUvfl5gAIHzA... If I counted correctly, you should be able to make a roughly rectangular shape out of the provided pieces. (Even if I miscalculated, I think they make a good exploration toy for the P2 tiling anyway.)
- samstave 8y agoYou will like this i assume: https://hyperallergic.com/416579/engare-game-islamic-design/ https://hyperallergic.com/416579/engare-game-islamic-design/ https://en.m.wikipedia.org/wiki/Girih_tiles https://en.m.wikipedia.org/wiki/Girih_tiles
- hexane360 8y agoI recently stumbled across this old site: http://www.mathpuzzle.com/ctrules.html http://www.mathpuzzle.com/ctrules.html I reverse-engineered the tiles in OpenSCAD. Let me know and I'll upload them.
- ryanmarsh 8y agoWould some enterprising HN’er please manufacture these? My wife would love this.
- phinnaeus 8y agoThey're available on the same site as the article: https://n-e-r-v-o-u-s.com/shop/line.php?code=12 https://n-e-r-v-o-u-s.com/shop/line.php?code=12
- zodPod 8y agoI can buy a 1000 piece puzzle for $5 at walmart. Sure it's not nearly as cool as this but 236 pieces for $120? That's outrageous. I'd rather just have my money, thanks.
- NickBusey 8y agoI can buy a 1000 piece chicken McNuggets for $5 at McDonalds. Sure it's not nearly as cool as a fresh local meal from a nice restaurant, but dinner for 2 for $120? That's outrageous. I'd rather just have my money, thanks.
- zodPod 8y agoAgreed? I mean, I think my comment makes it clear this way too expensive premium market isn't really the demographic that I fit into, though I know you're trying to prove a point. I do find it a little annoying that the internet has made it common to price based on the people who will pay the most for things. It is still just cardboard. Just because it's an interesting idea doesn't necessarily make 236 pieces of cardboard worth $120. To counter your point, this is like paying $120 for chick-fil-a nuggets instead of $5 for McDonald's nuggets. It's still just cardboard. It's slightly better made cardboard with maybe a little extra care, but it's just cardboard.
- NickBusey 8y agoTo counter your point, it is not just cardboard. It is laser cut wood. A far more expensive material, and manufacturing process.
- ballenf 8y agoThey appear to be hand-made. Manufacturing niche toys is very much a chicken and egg problem. At scale, these could be made for $1. But that implies volume sales which would likely result in a bunch of people complaining that the puzzles were "broken" and "some idiot left out all the edge pieces -- 0 stars!"
- 8y ago
- austincheney 8y agoI want to see a jigsaw puzzle that results in a mobius strip.
- lisper 8y agoJust take the Klein bottle one and change the shapes along the top and bottom (or left and right) edges so they no longer match up. Voila.
- 0xfaded 8y agoWell you’re looking at it. If you think of the puzzle only tiling in one direction, the flip needed to move the piece from one side to the other is analogous to the twist in the Möbius strip. Because it works in two dimensions, you have a Klein bottle, much the same way a looping plane is isomorphic to a torus.
- metalliqaz 8y agoI don't see how this is based on a Klein Bottle.
- rcthompson 8y agoIf you imagine the surface that is formed when every possible connection between pieces is made simultaneously, that surface is a Klein bottle. Obviously, making all the connections simultaneously is not possible in 3 dimensions, without allowing the pieces to deform and intersect each other.
- metalliqaz 8y agoDoes that property imply a Klein bottle? I was not aware they were synonymous.
- rcthompson 8y agoNot by itself. It could also imply a torus, depending on how the pieces must be oriented in order to fit each other. There may also be other possibilities.
- MrEldritch 8y agoA Klein bottle can be defined topologically as a Mobius strip that's connected on both axes. So if the left side is connected to the right side with a mirror twist, and the top is connected to the bottom with a mirror twist, it's topologically a Klein bottle.
- metalliqaz 8y agookay, I'm just not seeing how a puzzle with pieces that can be placed on the other side meets that property. The pieces would have to be elastic, and if the pieces are allowed to change shape, it's not really a puzzle anymore.
- rcthompson 8y ago
- rambojazz 8y agoVery interesting! With those curved borders however, it's going to be pretty hard to find where each piece fits :)
- tobr 8y agoCould someone who understands the topology of this more fully say - if I had a set of two or more of these, could I solve each separately and put the solved puzzles together into a larger pattern?
- gnarbarian 8y agofrom the article: > Multiple infinity puzzles can be combined to create a larger continuous puzzle. The image above shows some of the creative combinations possible with two infinity puzzles of different colors ($75, for two). here is the image from the quote: https://i2.wp.com/n-e-r-v-o-u-s.com/blog/wp-content/uploads/2016/11/infinity.png?resize=750%2C290&ssl=1 https://i2.wp.com/n-e-r-v-o-u-s.com/blog/wp-content/uploads/...
- tobr 8y agoSorry! I should’ve both read and expressed myself more carefully. I meant the Klein bottle topology, not the torus. EDIT: FWIW torus puzzles are definitely not a new thing - I had this one as a kid: http://img.tradera.net/images/096/270662096_95a37033-d8f9-4c3a-b874-37ab02db6e34.jpg http://img.tradera.net/images/096/270662096_95a37033-d8f9-4c...
- gnarbarian 8y agowell if anything from the left side can be flipped 180 and attached to the right side of the klein puzzle you should be able to assemble two copies in the same configuration, then flip one whole puzzle over 180 and attach it to the side of the other.
- nervous_jessica 8y agoNice! I haven't seen these before. There's also a brand of puzzles called Schmuzzles that are based on an escher lizard and tile. I would say the difference between these and our torus-based puzzles is that they employ a tessellation cut with repetitive piece shapes such that the image is guiding the construction (as all pieces fit in all places). In our puzzles, each piece only goes one place as they each have a unique shape. Our Klein Bottle and Cross-cap puzzles is are a new idea (to the best of my knowledge).
- chris_st 8y agoSo it's many (more than I want to admit :-) years since my Euclidean and Non-Euclidian Geometry class, but isn't this a cross-cap, not a Klein bottle?
- pgreenwood 8y agoNo cross-caps here. The first puzzle is a torus, the second a Klein bottle. Informally: the Klein bottle has on pair of edges is glued with a twist and one without; with the cross-cap, both pairs of edges are twisted then glued.
- chris_st 8y agoThanks for the reminder.
- nervous_jessica 8y agoThis one is a Klein Bottle but we just released a cross cap one yesterday: https://n-e-r-v-o-u-s.com/blog/?p=8068 https://n-e-r-v-o-u-s.com/blog/?p=8068
- Avshalom 8y agoSolid MEH, we bought my mom a jigsaw puzzle with no edges and the image (kittens) flipped on the opposite side in like... 94?
- andreareina 8y agoHow does one map an existing locally-similar pseudorandom pattern like the galaxy image onto a torus, Klein Bottle, or other closed shape? I know that with a generated pattern (e.g. Perlin noise) you automatically get that by taking the value of the noise function at the surface coordinates, but I have no clue about using existing planar images.