Hyperbolic Crochet Motifs

Need an explanation? Thought you might and here you go: “Hyperbolic Crochet is the name given to applying a mathematical principle to crochet patterns. A hyperbolic plane expands exponentially from any point on its surface, always curving away from itself. Hyperbolic growth gives rise to the ruffled shapes of coral, kelp, and sea anemone. You can easily crochet a hyperbolic surface by increasing at a constant rate throughout the piece. Crocheting a reef is a great opportunity to try different yarns and stitches. The variety of textures and shapes will inspire you to expand your crochet boundaries.” (quoted from Lionbrand)

Thanks to everyone who sent this in…yikes, just what level has Lionbrand sunk to with this one? Bottom of the ocean low? Not sure you can get much lower than that.

54 Comments to “Hyperbolic Crochet Motifs”

  1. It’s an interesting math lesson. But . . .


    Maybe we can use crochet to fix the Great Barrier Reef. At least then people wouldn’t have to look at it directly.

    • 4 years down the track from the original post, does anyone still feel the same? The Lion Brand project is of a dead reef; its already far too close to reality for comfort! It was never about fashion or even art – its a synthesis of maths and crochet that happens to have come to represent the damage we are doing to our environment. Now that that mini reefs made from recycled materials are being sold on Etsy perhaps the people who wrote the earlier comments might like to retract them?

  2. what a waste of what looks like some nice yarn. Might be good for your crappiest yarn remnants–but even then, why? Stick it in your aquarium?

  3. That, or mimicking the stuff I need to clean out of my fridge that’s causing a God-awful smell in that part of the house. . .

  4. I don’t think Lionbrand is responsible for this one.


  5. Trish: if you want someone to blame, blame Daina Taimina.

    Two points in Dr. Taimina’s defense: first, if we approach this from the point of view of seeking a visualization for this mathematical curiosity, rather than trying to build aesthetically pleasing crochet, it’s actually very clever; most attempts at producing a realspace embedding of the hyperbolic plane are fragile and useless. The crochet one is pretty nifty because it’s durable and can be used to illustrate some geometrical concepts (for instance, a “line” on the hyperbolic plane curves around away from the node; fold one of Dr. Taimina’s crochet models and the curvature of the folded “edge” becomes apparent). The second point in her defense is that this geometrical curiosity has in fact been used in an artistic context, although to a lesser degree; some work with scalloped or frilly edges is produced by extraordinary numbers of increases on a single row or round, and this produces frills through, to put it in a mathematical context, the embedding of negative curvature in Euclidean space. So while a hyperbolic manifold as a hyperbolic manifold is of more interest as a mathematical construct than as an artistic creation, the underlying principles are used in real crafts.

    • The technique of large numbers of increases row to row has been used for ages to create flounces and ruffles in crochet. Dr. Taimina realized that it was a way to visualize a mathematical concept and she should be remembered for this and thanked for making the connection between “women’s work” and science.

  6. Well I have to disagree with you guys on this one. It’s pretty much the basis for my crochet work… sigh. Ahh well. You can’t win ’em all.

  7. Actually… as a teacher, I would do almost anything to pique the interest of my students, and I’ve even used yarn to do that with kindergarteners. So, although I don’t find it pleasing to the eye, I *do* find it interesting. Count this as a negative cringe? 😉

  8. I don’t think the concept is a bad one, but that happens to be a pretty fugly implementation.

  9. Let us not confuse science and fashion. You wouldn’t wear a model of the solar system on your head or an anatomical dummy on a pendant around your neck. I wouldn’t, anyway. But that doesn’t mean you couldn’t put these little crochet-fungi on the classroom windowsill next to the solar system and the dummy to collect dust for the next twenty years unitl it’s offered to befuddled PTA members at the school rummage sale for 25 cents and is finally tossed into the trash.

  10. i love the lion brand newsletter… it’s filled with gems like this that make me go WTF? and then laugh my ass off.

    i think crocheted coral is cool… but i’ve seen real coral.. it’s not khaki, it’s breathtaking colors, mostly neon… it’s just when you try to photograph it that it comes out khaki… maybe that’s what happened when lion brand took pics of their crocheted coral?

    • Actually the Hyperbolic Crocheted Coral Reef which has been shown in Chicago, New York, London, Los Angeles and in 2010 in Washington, D.C. (at the Smithsonian!!!!) has brilliant color and masses of reef pieces sewn together. The white/grey/beige pieces are, however, excellent examples of sick and dying coral reef.

  11. There’s a fungus among us!

  12. To Jake: ouch, my head hurts! No wonder math was no fun in school.

  13. I’m with Liz on this…

    Crocheted coral – pretty cool idea (but I went to a marine biology school as an undergrad)

    Crocheted coral in khaki? – a big WTF there. The other online photos of the crocheted coral are vibrant and fun. Would be a great educational tool in the classroom or at an aquarium.

  14. Well I guess I can see how some people dig this, but this has got to be a very speciallized thing.

    I think that for the most part, this is pointless. I mean, talking about it is one thing, but actually doing it is another.

    We get the idea. We’re not children in need of hands-on learning experience to understand the concept.

  15. It’s kind of like the knit Ferrari or Christmas scene…only they know it’s true purpose….SIGH

  16. This is actually part of a knitting and crochet project from the Institute for Figuring. They are actually creating a coral reef in yarn. They didn’t say why, but I think they’re just attempting to express a mathematical principle in a concrete fashion. Didn’t say I like it, but that’s what it’s for.

  17. I still think it’s the mate of the squid hat.

  18. I agree with Jake. This was a brilliant idea, to use crochet to model a hyperbolic plane, an excellent example of the rising influence of women in mathematics , not to mention a tribute to the needle arts. Think about it: a skill that was once viewed as a trivial pastime of “the weaker sex” is now used to understand a mathematical theory that is applied in the solution of real world problems of many sorts. Whether you like the idea of crocheting a reef or not, the REAL ISSUE here is that Lion Brand ripped off Daina Taimina’s idea. When Lion Brand first posted the reef pattern on their website, it read as though someone at Lion Brand had come up with the idea of crocheting a hyperbolic plane (obviously one of their staff of experts versed in non-Euclidean geometry). There was no mention of Dr. Taimina or the Institute for Figuring (where the reef idea originated). So I wrote an email to the Institute for Figuring (and I wouldn’t be surprised if others did the same) and told them I hoped they were receiving a royalty, or at least some free yarn, from Lion’s use of their idea. About a week later I received a reply from the Institute saying that Lion was “rectifying the omission”. Lion did add information about the Institute for a period of time, but it’s not there now. It really ticks me off when corporations steal the ideas of individuals.

  19. While I like the LB reef OK, the real one (ok, the real recreated in yarn one!!) is quite amazing. See and read about it here: http://www.theiff.org/reef/index.html

  20. “Let us not confuse science and fashion.” First off… if it weren’t for the science, we wouldn’t have the fashion. And who says this was made to be worn? Not everything that is crocheted has to be worn. This was clearly an artistic attempt, and I think it’s an interesting concept which is used CONSTANTLY in fashion. Though this particular outcome isn’t “pretty”.

    Has anyone seen the crazy hats of Anna Voog? They are inspired by sea anemones and such. Very cool. http://www.anacam.com/hats/

  21. My understanding of this hyperbolic crochet coral reef project is that it’s about getting people to realise that real coral reefs are dying (or bleaching) & we need to do something about that. The reefs are already damaged by the increase in seawater temperature so far, another few degrees & the crochet reminders will be all we have!

    Now we wouldn’t want that to happen or we (or our mokopuna) will be looking at crochet coral in museums & saying how careless their tipuna were with the planet.

    Kia ora

  22. Shouldn’t creativity be encouraged? As for copying, why do you think several magazines all feature recipes for chocolate cake in the same month, or numerous shops all put the same style of blouse on display within a few weeks of each other – we’re all exposed to the same influences! Lighten up people – nothing suits everyone. Leave some room for crochet enjoyment without harsh critical words.

  23. I think that your outlook is very close minded. Incredible freeform crochet has revitalized the art of crochet. This seems to be all ‘granny’ opinions – as outdated as the granny square.

  24. Hmm. This is my first visit to whatnottocrochet, and I have to say I was really surprised to see that hyperbolic reef crocheting — even Lion brand’s fungi-tone attempt — made your list. I find I’m wondering what you think IS a good use of crochet, especially since I find most of the patterns in even the higher-end new books truly fug ugly….

  25. What do you do with this when it collects dust? Do you throw it in the washer, and take the chance that it *gasps* loses its shape? I really don’t see the point of hyperbolic crochet, but whatever sells the yarn. But what a waste. You could use it to make hats for newborn babies in third world countries.

  26. A very cool follow up. This is a free display in my local area. Crochet and protest but all in the name of raising awareness, bringing new young needle crafters together and cleaning out the stash of neon yarn and that odd ball of fun fur. You know what I’m talking about!
    Chicago Reader | Our Town: Crocheters Gone Wild By Tasneem Paghdiwala

  27. Okay, the part of me that likes math finds that description veeeeery insulting.

  28. i can’t think of any purpose for crochet mushrooms.

  29. God, some stuff is just plain – horrible yet hysterically funny!
    However with the hyperbolic stuff…….I like it. And have a look at this if your interested.
    This really is not about decorating yourself or your house. It’s about raising awareness of the destruction of the Reef.
    Look at us……we are commenting so we are aware and might think to do something or support a cause that is doing something

  30. Sorry. My inner geek loves this. Maybe you could fault someone for not selecting more realistic yarn colors, but I think this is really fun. I bought an old crochet doily that was obviously created using these mathematical concepts. Not for everyone, or for every occasion, but I think it’s very creative and interesting and cool. And Anna Voog is a riot! Great, crazy work.

  31. What a shame you used such a dull picture to illustrate the project. I have seen the exhibition of the crochet coral reef in London and the colours and textures are stunning. Parts of the ‘reef’ are made out of plastic bags, magnetic tape and other detritus from the Thames in surprisingly effective ways.

    People leaving comments like ‘yuk’, ‘horrible’ and ‘what’s the point’ need to get out more and exercise their imagination.

    And I now understand hyperbolic geometry!

  32. The exhibition is fantastic and the Crochet Reef is a very good idea. It’s about recycling materials and the colours they’ve used are amazing. Go and see if you can.

  33. The “all white” colorway is just one small section of the exhibit, and the picture you chose actually depicts the problem of “Coral Bleaching Events” caused by the warming of ocean waters. These events used to occur once per decade or so, but now occur nearly annually with 2009’s expected to be the largest ever. It indicates stressed corals, sort of canary in the mineshaft style. Also, the “all whites” are a small vignette in this extraordinary colorful and amazing showing, (which is going to the Smilthsonian in 2009, the same Smithsonian that has NEVER mounted an art show previously).
    There is way more to this than you gave it credit for– The Reefs project has actually become an artistic/environmental movement, with community Reef projects springing up all over the world and being added to the show, mounted with Margaret Wertheim’s original Reef – from New York, Chicago, Scottsdale, Latvia, London, etc. This project depicts technology, entertainment, and design applied thru the lowest of tech (a crochet hook) paired with higher mathematics — the patterns are derived from non-Euclidian hyperbolic algorythms. It’s totally great!

  34. I agree with Sariella and Liz. What’s wrong with exploration and imagination?

    Crochet doesn’t have to have only practical uses – i love the idea that it can be art form. I like hyperbolic crochet. I wish I’d seen the exhibition.

  35. I participated making pieces for the New York City Coral Reef, which was on show at the World Financial Center for several months. If you think about it, traditional flounces and ruffles are hyperbolic crochet and we’ve been using the technique for a long time. This project involved seeing the work as ART and as a different creative way to use crochet.

    As I read through the comments here, I made some replies to previous posters.

    This was my first reply: Actually the Hyperbolic Crocheted Coral Reef which has been shown in Chicago, New York, London, Los Angeles and in 2010 in Washington, D.C. (at the Smithsonian!!!!) has brilliant color and masses of reef pieces sewn together. The white/grey/beige pieces are, however, excellent examples of sick and dying coral reef.

    I’m in the process of creating a series of panels to hang in my home. It really can be look quite beautiful.

  36. its absolutely beatiful! perfect.

  37. They make neat cat toys.

  38. this is actually a fascinating concept, you should look more into it.
    granted, this “artists” interpretation of hyperbolic crocheting is pretty poorly executed. However, there are other women who crochet coral reefs for a living. they make these reefs and sell them as a works of art to museums. i think thats a pretty amazing job. just google it, if your interested at all in crocheting at all i think it will interest you. dont give up on hyperbolic crocheting yet! heh

  39. Boring I think would probably describe this image, but crap probably not.
    It has been an influential technique amongst fibre artists amongst the world and many large scale installation works have been conducted.

  40. An old thread but I love it and can’t wait to see it at the Smithsonian. I had fun with making a bath pouf using the technique. Made a great ball for a baby too…lots of little places for tiny fingers to grab.

  41. I love this! I have a new born grand daughter and am going to make her a ball of this! It’s scientific, lovey and soft and made by Grandma Darla! Beat that! Can’t wait for her to be old enough to play with it!

  42. I think its amazing! And where do u find that squid hat my daughter would love it!! 🙂

  43. I’m with the “crazies” here. As somebody who’s done more than a little math in my day I’m a big fan of Hyperbolic crochet. In fact I use it to make flowers for various plant based Amigurumi, as it produces some very unique looking and complex blossoms.

    I’ve always disagreed with the tennat that all yarn should be used only in useful application. Should painters only use paint for covering walls? Is there no room for pure aesthetic application of yarn?

    As for the comment about the dust and risking the piece being washed. Perhaps that is a risk worth taking, no? And perhaps that risk is one the artist has decided to live with.

    All that aside, the Khaki only implimentation kind of misses the mark of what hyperbolic crochet can really do and really does deserve to be shown here. It’s ugly and dead looking; fugly? But, I’ve seen colorful implimentations that were truely stunning to behold so I find the method above the reproach it was given.

    C’est la Vie,

  44. I think the coral crochet is really cute and looks pretty too. I know most of the stuff you post is rather hideous – like those dog papoose things they made me crack up laughing!! – I guess it’s your opinion if you don’t like it. I’m gonna go along to the hyperbolic crochet workshop next month in Adelaide. I’ve just being going through all your posts and I love some of them- like the man thongs!! I should so make one for my boyfriend, he’d most likely jump out the window

  45. I’m with the “crazies” as well. In fact, I am disappointed by this post. I had the opportunity to see the Crochet Coral Reef at the Natural History Museum in DC, and was awed by the amazing scale of the project (in that it took up the back part of the sizable Ocean Gallery). It was gorgeous in so many ways, including:

    1. The practical interpretation of a type of geometry not readily understood by most (including me!).
    2. The fact that is brings attention to the global plight of coral reefs.
    3. The notion that so many small, individual forms created by people throughout the world combined in a most elegant, impactful, and yes, beautiful way.

    Someone needs to pull their head out of the sand (and from some of these responses, I can see that more than one needs a little more education in the Arts, Mathematics, and Natural Sciences).

    • You are soo right!

      I am definately gonna try this at home, as ecotoxicologist working with marine issues I kinda have to. It is wonderful that one of my favourite in-front-of-the-tv-activities has scientific applications as well. I wish they had taught maths at school using such techniques… Actually, it’s impressive that hyperbolic planes were known for about 200 years before someone came up with the idea of using crochet to visualize these planes!

  46. Although I agree that some of the items in the above picture are not attractive, the spherical shaped one can be used as a scrubbie. Just chain 2, 6 singles in the first chain, then just place 2 sc in each sc until you reach the desired size. No joining. Nice, soft scrubbie for your baths or showers—–similar to the netted sponges you buy, but yarn is washable!

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