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Crochet Hyperbolic Coral reef Project


The Institute For Figuring is crocheting a coral reef: a woolly celebration of the intersection of higher geometry and feminine handicraft, and a testimony to the disappearing wonders of the marine world.

Designed and curated by IFF co-directors Christine and Margaret Wertheim

Crocheted “mega coral” by Christine Wertheim.

One of the acknowledged wonders of the natural world, the Great Barrier Reef stretches along the coast of Queensland like a psychadelic serpent, a riotous profusion of color and form unparalleled on our planet. But global warming and agricultural pollutants so threaten this fragile monster that scientists now believe the reef will be dead in 30 years. As a homage to the Great One, the Wertheims - who grew up in Queensland - have instigated a project to crochet a woolen reef. Using the techniques of hyperbolic crochet discovered by mathematician Daina Taimina, the Institute has been evolving a wide taxonomy of reef-life forms - loopy "kelps", fringed "anemones", and curlicued "corals." Though the process that brings these models into being is algorithmic, endless permutations of the underlying formulae result in a constantly surprising panoply of shapes. The quality of yarn, style of stitch and tightness of the crochet all affect the finished model so that each is as individual as a living organism. The reef is made up of four sub-reefs, each with its own colors and styling and each evoking a particular strata of marine life: the kelp section (green/grey), coral section (orange), anemone section (blue/black), and the "ugly" section (purple). Like its biological counterparts, the crochet reef grows slowly: each piece is hand-made and individually thought out.

Crochet Hyperbolic Reef Gallery

Crocheted “anemone”, made by Margaret Wertheim.
Each model results from the application of an iterative recipe repeated over and over. Like fractals such as the Mandelbrot Set, these forms come into being only through the process of doing some “boring” step again and again and again. Though experience often serves as a guide, there is no way to know in advance what a specific algorithm will achieve and we have many times been surprised when seemingly insignificant changes in the underlying pattern have led to fundamentally new results. This is, in a very real sense, a kind of experimental mathematics and we invite crocheters everywhere to join us in exploring the myriad possibilities inherent in these techniques.

For more indepth information, see the Institute's book A Field Guide to Hyperbolic Space.
Crocheted “striated coral” made by Daina Taimina, with “brain corals” by Spring Pace.
Getting started on your own hyperbolic models is easy. The basic insight is to understand that these forms result from the simple process of increasing the number of stitches in every row. The more often you increase stitches the faster the model will grow and the more crenellated will be finished form. Models can begin with a simple line, resulting in a hyperbolic plane; or from a single point with the crochet spiraling around to gradually fan out like a cone, resulting in what is known as a pseudosphere. You may also begin from a circle, which will produce a tubular, bell shaped, or trumpeted configuration. Once you start to experiment, the variety is endless. We recommend that beginners read the IFF’s online exhibit on Hyperbolic Space and study the introductory gallery for helpful tips.

A crocheted strand of kelp, made by David Orozco.

As you explore, be playful – don’t worry about sticking too closely to the formal rules, though it’s interesting and important to understand what the rules do. Try things out for fun. Experiment with different types of yarn. Try mixing yarns together, say a thick worsted and a fine mohair. Try varying the rate of increase in a single model. Consider using string, plastic and wire or anything else that takes your fancy. Try felting – throw the finished model in a washing machine with really hot water and let it churn for half an hour. This only works with pure wool (acrylics and cotton will not felt) but the results are wild! Finally – send us photos of your models and we will put them online in our People’s Hyperbolic Gallery.

Get involved
We invite crocheters everywhere to contribute models to the reef. This is a collective project and all contributors will be fully acknowledged online and in future exhibitions. If you want to send a model please contact us by .