Written by: Brianne Davis, Gallery Assistant


In 2003 sisters Margaret and Christine Wertheim founded the Institute For Figuring, the focus of which is to increase the public’s understanding of scientific and mathematical themes many of which focus on the environment. Two years later they began their best known project, the Crochet Coral Reef project. The yarn creations first mimicked the structure of the Great Barrier Reef as homage to the marine. Coming from Queensland, Australia, a country surrounded on all sides by the ocean, the health and condition of the aquasphere is deeply embedded in their daily life and consciousness. To create the curling, free flowing shapes they used and adapted the technique discovered by Dr. Daina Taimina, “hyperbolic crochet.” “Loopy “kelps”, fringed “anemones”, crenelated “sea slugs”, and curlicued “corals” have all been modeled with these methods” (Institute For Figuring).

The hyperbolic crochet technique creates a basic foundation for forms, but the flexibility of the algorithm allows for near endless variety. Thus, as the Crochet Coral Reef project began expanding into different cities and countries “an on-going evolutionary experiment in which the worldwide community of Reefers brings into being an ever-evolving crochet “tree of life”” (Institute For Figuring). The variations of the reefs go beyond colour and form; different reefs have also begun incorporating new materials. One of the most spectacular uses of new materials is the Bikini Atoll project, lovingly nicknamed “The Toxic Reef.” In response to the Great Pacific Garbage Patch, the project interweaves yarn and large amounts of plastic trash. The project highlights the growing amounts of plastic trash that are becoming embedded in and choking out the underwater environment.

Source: Forward Council

To date the project has grown exponentially. From the Wertheims’ home it has grown into a multitude of sub-reefs in satellite locations along with travelling exhibitions and events. The first satellite reef was the Chicago Reef hosted by the Jane Addams Hull-House Museum and the Chicago Humanities Festival in 2007. Since then 36 satellite reefs having been created in total spanning the globe primarily in the United States of America and Australia and have spread as far as Germany, Japan, and Croatia. The most recent project exhibition is Crochet Coral Reef: CO2CA CO2LA OCEAN at the Mary Porter Sesnon Art Gallery, UC Santa Cruz (February 10 – May 6, 2017). In addition to the exhibition, the campus will also be creating a satellite reef by students, faculty, staff, and members of the Santa Cruz community.

Satellite Reef Locations

Artists have often been the ones to hold a mirror up to the world, exploring those issues that are most pressing in society. Environmental issues have long had a strong foot-hold in the realm of fine craft, exploring the interconnectedness of nature, humanity, and the fine balance that sits between the two. The Crochet Coral Project is just one of many recent exhibitions to focus on the ways that humans have effected change in specific habitats. The Saskatchewan Craft Council exhibited Monique Martin’s show Continuous, the focus was on another keystone species: bees. Upon entering the gallery visitors were greeted with the sounds of an active hive, the smell of beeswax, and prints hanging from the ceiling with images of bees scurrying across the honeycomb. As you moved through the gallery the prints moved from image of a healthy hive to those in successive states of decay. The show explored how society has impacted bees, as in recent years there has been much focus on the decline of bees in nature. Bees are a keystone species, meaning that they are one that many other species rely on and can serve as a general barometer of the overall health of an ecosystem. The shows both address the issues of how these environments are suffering and the way the damage reflects on society.

How to crochet an annular hyperbolic plane as explained in the article “Crocheting the Hyperbolic Plane” by Dr. Taimina, updated by David W. Henderson:

It is recommended that the yarn chosen has minimal stretch, allowing the crocheted piece to maintain its shape will be important for the end result.

Figure 2. Crochet stitches for the hyperbolic plane. (Source: Taimina and Henderson)

  1. Make your beginning chain stitches (Figure 2a). (Topologists may recognize that as the stitches in the Fox-Artin wild arc!) About 20 chain stitches for the beginning will be enough.
  2. For the first stitch in each row insert the hook into the 2nd chain from the hook. Take yarn over and pull through chain, leaving 2 loops on hook. Take yarn over and pull through both loops. One single crochet stitch has been completed. (Figure 2b.)
  3. For the next N stitches proceed exactly like the first stitch except insert the hook into the next chain (instead of the 2nd).
  4. For the (N+1)st stitch proceed as before except insert the hook into the same loop as the N-th stitch.
  5. Repeat Steps 3 and 4 until you reach the end of the row.
  6. At the end of the row before going to the next row do one extra chain stitch.
  7. When you have the model as big as you want, you can stop by just pulling the yarn through the last loop.

Be sure to crochet fairly tight and even. That’s all you need from crochet basics. Now you can go ahead and make your own hyperbolic plane. You have to increase (by the above procedure) the number of stitches from one row to the next in a constant ratio, N to N+1 the ratio determines the radius (the r in the annular hyperbolic plane) of the hyperbolic plane. You can experiment with different ratios BUT not in the same model. You will get a hyperbolic plane ONLY if you will be increasing the number of stitches in the same ratio all the time.

Crocheting will take some time but later you can work with this model without worrying about destroying it. The completed product is pictured in Figure 3.

Figure 3. A crocheted annular hyperbolic plane. (Source: Taimina and Henderson)


Forward Council. “The Hyperbolic Crochet Coral Reef by the Institute For Figuring.” Curated Items. http://forwardcouncil.com/curated-items/34/the-hyperbolic-crochet-coral-reef

Institute For Figuring. “About the Project.” Crochet Coral Reef project. http://crochetcoralreef.org/about/index.php

Institute For Figuring. “Satellite Reefs.” Crochet Coral Reef project. http://crochetcoralreef.org/satellite/index.php

Institute of the Arts and Sciences. “Crochet Coral Reef: CO2CA-CO2LA Ocean.” University of California Santa Cruz. http://ias.ucsc.edu/content/2017/crochet-coral-reef-co2ca-co2la-mary-porter-sesnon-art-gallery

Taimina, Daina, Henderson, David W. “Crocheting the Hyperbolic Plane.” Mathematical Intelligencer, 23, No. 2, (2001): 17-28. http://www.math.cornell.edu/~dwh/papers/crochet/crochet.html