Created and Curated by Margaret and Christine Wertheim of the Institute For Figuring in Los Angeles

Between the 20th of March and June 11th, 2010, over 50,000 visitors came to the Science Gallery. Many came away inspired to take up crocheting, learn more about hyperbolic geometry or to explore the secret underwater world of corals.

One of the acknowledged wonders of the natural world, the Great Barrier Reef stretches along the coast of Queensland, Australia, in riotous profusion of colour and form unparalleled on our planet. But global warming and pollutants so threaten this fragile marvel it now faces devastation, along with reefs around the world. In homage to these disappearing treasures, Australian sisters Christine and Margaret Wertheim instigated a project to crochet a handmade reef, a woolly testimony that celebrates also a strange geometry realised throughout the oceanic realm.

In coral reefs we witness an endless whimsical diversity – loopy kelps, fringed anemones, crenellated corals, curlicued sponges. All these forms are variations of a mathematical structure known as hyperbolic space. Though mathematicians had long believed this space was impossible, nature has been playing with its permutations for hundreds of millions of years. In 1997, Dr Daina Taimina of Cornell University realised how to make models of this geometry using the art of crochet. Building on Dr Taimina’s techniques through  elaborations of her original crochet code, the Wertheim sisters have spent the past five years developing an ever-evolving taxonomy of reef-life forms.

Tightly bunched mounds of brain coral, wavy strands of kelp, tubeworms, sea slugs and nudibranchs have all been mimicked with the twins’ techniques. Just as the diversity of living species results from variations in an underlying DNA code, so too a huge range of hyperbolic crochet ‘species’ may be brought into being through modifications in the underlying crochet code. There is an ever-evolving crochet ‘tree of life’.

Anyone who takes up these techniques can begin to develop their own woolly species and the Crochet Reef is a communal project. The community of Reef Contributors now spans the globe with participants coming from across the USA, as well as Australia, England, Ireland, Latvia and Japan. Taken as a totality, the project has become an unexpected, global, evolutionary experiment that engages people around the world.


As a communal endeavor the Hyperbolic Crochet Coral Reef seeks to include people from all walks of life. To date over 3,000 women and a few men have contributed models. In cities where the ‘Core Reef’collection is shown – as here in the Science Gallery – Margaret and Christine work with local communities to make their own ‘Satellite Reef’. Satellite Reefs have now been made in Chicago, New York, London, Arizona, Sydney and Latvia. The newest addition to this growing archipelago is the Irish Reef, which is making its debut at Science Gallery.

Also on show here is most of the Latvian Reef which was produced during 2009 by more than 600 women and school students across Latvia. The Latvian Reef was spearheaded by Tija Viksna, a handcrafter in Riga. Other satellite Reef initiatives are currently underway in Melbourne, Perth, Indiana, Fukuoka and Capetown. The totality of these local initiatives is known as The People’s Reef and it is hoped that one day this vast outpouring of citizen creativity will be exhibited together as a whole.

The Reef Project engages expert crocheters and beginners alike. Participants so far include a sheep farmer in rural Australia (Helen Bernasconi), a science fiction writer in Seattle (Vonda N. McIntyre), a geophysicist in Santa Cruz (Heather McCarren), and a Hungarian costume maker in Liverpool (Ildiko Szabo). Among the Core Group of the Reef’s most committed contributors there are academics, mothers, mathematicians and students. While engaging women in a handicraft with which they feel comfortable, the Crochet Reef leads us into the worlds of mathematics, marine biology and two of the most pressing ecological issues of our time – global warming and the escalating tragedy of plastic trash in our oceans.



In the Pacific Ocean north east of Hawaii a vast island of plastic trash is accumulating. Known as the Great Pacific Garbage Patch this floating mass of debris is now twice the size of Texas and more than 30 metres deep. The Garbage Patch is formed by a natural confluence of ocean currents that spiral into a vast slow-moving vortex in this region. Every year humanity produces more than 100 million tons of plastic, of which it is estimated that 10% ends up in our oceans. Most plastics do not biodegrade but break up into fine particles forming a kind of part of the Hawaiian chain, beaches are periodically inundated by this toxic mess. In the ocean these particulates eventually sink to the sea floor where they will be embedded in the geological strata of our planet forming a permanent plastic layer. Meanwhile plastic trash kills an estimated million sea birds every year, along with 100,000 marine mammals.

A major element of the Crochet Coral Reef Project is its ‘plastic component’ which responds to this crisis. Where the yarn-based Reefs serve as a handicraftplastic sand. In the northern invocation of the living beauty of actual reefs, so the “Toxic Reef” is a wildly proliferating agglomeration of yarn and plastic trash. It is the ‘evil’ 21st century twin to the classical finesse of the yarn Reefs. To put this into temporal terms, we might say that where the yarn Reefs represent the past, and the exquisite creations of nature, the plastic looks to the future and to the destructive tendencies of humanity.





When we started crocheting corals it never crossed our minds they could actually be in water. It took the brilliance of industrial designer Kathleen Greco and her patented Jelly Yarn thread to make the transformation to an aquatic environment.



Made by Sydney crafter Helle Jorgensen, the “Rubbish Vortex” is crocheted entirely from used plastic shopping bags donated from around the world. The bags are beginning to degrade, an elegaic proof of what happens in the ocean.



A forest of kelps made from discarded video-tapes by Christine Wertheim and Evelyn Hardin. Millions of miles of video tape have been thrown away as we move to the DVD age. How many more iterations of imagery is humanity going to discard?



A flock of jellyfish made from plastic bin-liners by Margaret Wertheim. These are the liners that fill trash bins in offices and waiting rooms the world over.



A grove of corals crocheted around discarded plastic water bottles by New York crafter Nadia Severns, a committed environmentalist and professional knitter, who made many of the brightly coloured sweaters worn on The Bill Cosby Show.



Made from electroluminescent wire used by the US military to light the insides of tanks, these pieces were constructed by the Reef’s oldest contributor, Eleanor Kent, a 78 year-old media artist in San Francisco. When current flows through the wire the plastic coating fluoresces. Eleanor calls this her ‘granny-tech’.



Playfully referring to one of Andy Warhol’s happenings, the Plastic Exploding Inevitable Reef is Christine’s pop-art fantasy. It features hot-pink Jelly Yarn sand and kelps by Kathleen Greco, who invented this special vinyl thread for knitting and crocheting.



Made from the blue plastic wrappers of the New York Times, embellished with straws and medical waste, the Blue Grove is the creation of Los Angeles librarian Clare O’Callaghan who has been collecting plastic trash for over 30 years.



Featured in the Toxic Reef are also plasticshopping- bag anemones by UK Reefer Luncinda Ganderton plus “Midden Monsters” by Evelyn Hardin, saran-wrap anemones by Pate Conaway and an elegant trash Bottle Tree by Barbara Wertheim, Margaret and Christine’s mother.


One could be mistaken for thinking these delicate forms were marine diatoms, but they are crochet doily patterns. The work is made by Sarah Simons, the Crochet Reef’s first formal contributor after Margaret and Christine and one of the project’s most creative taxonomical innovators. Sarah is an expert crocheter, knitter and beader who also delights in mastering new kinds of computer software. A native Los Angeleno, Sarah helps run the IFF’s sister organisation, the Centre for Land Use Interpretation.

(The animation is showing in the café)




The distinctive crenellated forms of the Hyperbolic Crochet Coral Reef are variations of a mathematical structure known as hyperbolic space. This aberrant geometry is an alternative to the canonical flat or Euclidean geometry that we learn about in school and the spherical geometry that represents the surface of our earth. Mathematicians spent hundreds of years trying to prove that anything like hyperbolic space was impossible only to discover in the nineteenth century that the laws of mathematics necessitated this form.

In 1997 Dr Daina Taimina discovered that it was possible to model hyperbolic space using crochet, an innovation that surprised the mathematical world. Her geometrically precise models are now used to help introduce university students to the subject of non-Euclidean geometry, the mathematics that underlies general relativity and which will therefore help us to understand the structure of our universe.

Mathematically, the three geometries may be understood by the behaviour of ‘parallel’ lines. On a Euclidean surface parallel lines stay the same distance apart forever. On a spherical surface all parallels intersect – think about the lines of longitude meeting at the poles of our earth. On a hyperbolic surface, parallel lines diverge. Where spherical space has positive curvature and flat space has zero curvature, hyperbolic space has negative curvature – it is the geometric equivalent of a negative number. The unique properties of this geometry were a source of fascination to the Dutch artist M.C. Escher, whose Circle Limit series of woodprints explore the rich tessellations possible within this space.

Nature also delights in the hyperbolic form but does not feel compelled to realize geometrical perfection. Just as there are many things in nature that are spheroid, such as eggs, but no such thing as a perfect natural sphere, so too the organic world abounds in not-quite-pure hyperbolic structures. The Hyperbolic Crochet Reef Project takes its cue from this domain of organic ‘imperfection’.


Perhaps the most elegiac aspect of the Reef project is the Bleached Reef, a crochet invocation of coral bleaching. When corals get stressed a phenomenon known as bleaching occurs in which large sections of reef turn white. Over the past two decades coral bleaching events have been increasing in magnitude and frequency around the world as a consequence of increasing sea temperatures due to escalating levels of atmospheric carbon dioxide. In addition to causing rises in water temperatures, CO2 also causes seawater to become more acidic, leading scientists to talk about the ‘Coca-Cola ocean’. Acidic waters impede the formation of coral exoskeletons and some scientists predict that if current trends continue corals may no longer be able to build these structures at all by the middle of this century.

The Bleached Bone Reef features works by some of the Project’s most technically skilled crafters including beaded sea creatures by Nadia Severns, Jill Schreier, Pamela Styles and Vonda N. McIntyre.



In the history of the Hyperbolic Crochet Coral Reef Project, the mysterious “Dr Axt” has been a singular force. Over the past four years this enigmatic Seattle-based artist has created three giant coral mounds of exceptional beauty and scale. Collectively she calls them her “Reefer Madness” project. Hanging near the stairs we see her original installation, “Reefer Madness”, in red and pink and blue (from 2006), plus a brand new work, “Pinkus Yellownicus – Mermaids Wedding Cake”, (from 2009/2010). In the gallery upstairs is “Whiticus Reeficus”, the good Doctor’s personal response to coral bleaching (from 2008/2009).


Imagine a Victorian Lady, a vital young adventurous woman who dreams of the South Sea Islands. She has read the journals of the great Pacific explorers but is destined instead by her parents and society to a Great Marriage. She and her companions spend their afternoons crocheting their own coral reef, a feminine invocation of the natural wonders they have read about in books. Definitively referencing the domestic roots of handicraft, the Ladies Silurian Atoll has been made by a small and intimate group of the Reef’s most dedicated contributors.

This delicate ‘fancywork’ marvel evolved within the private space of Margaret and Christine’s living room, where for several years it remained the dominant life form in their house. This delicate ‘fancywork’ marvel evolved within the private space of Margaret and Christine’s living room, where for several years it remained the dominant life form in their house.



The White Spire Grove is crocheted by Dallas contributor Evelyn Hardin, our favorite Mad Texan. Evelyn, a master of new and old materials, has incorporated into this work seed-pods, Christmas decorations, hair ornaments, drinking straws and plastic flowers. The long white pillars were inspired by deep-sea tube worms, and the spiral forms unconsciously evoke narwhal tusks. The White Spire Grove was curated by Ann Wertheim.




by Mieko Fukuhara

Mieko’s tiny staghorn corals are crocheted out of mercerized cotton thread, which was traditionally used for making doilies. Her exquisitely detailed forms are modeled on a classic coral species that is now seriously endangered.



by Anita Bruce

Knitted and crocheted out of scientific wire, these sea creatures are crafted by English computer programmer Anita Bruce. Anita has created a Darwinian taxonomy of these forms, which were originally devised for her thesis project for a Bachelors Degree in Fine Arts, an endeavor she began in her forties.



by Arlene Mintzer

“The Garden of Aqua Flora” constitutes an extensive fantasy by New York fibre artist Arlene Mintzer. On show here is a small sample of Arlene’s work stacked into miniature Gaudiesque towers.



by Nadia Severns

Nadia Severns – a master beader and knitter from upstate New York – transforms the irritant grains of refuse into handicraft pearls. Inside each of her beaded forms is a piece of throw-away plastic trash.



by Ildiko Szabo

One of the Reef’s first contributors, Ildiko Szabo is a theatre costume maker in Liverpool, UK. Ildiko hails from Hungary and her inimitable sense of form and colour make her the Reef’s reigning pop-art queen.



by Helen Bernasconi

A former computer programmer, Helen Bernasconi now lives on a farm in the Australian state of Victoria. Helen raises her sheep, shears them, spins the wool and hand-dyes the yarn. She invented the “octopus” form whose tentacles are hyperbolic “curlicues”.



by Heather McCarren

Heather McCarren created a pale-pink grove of tube anemones while working on a PhD in geoscience at the University of California, Santa Cruz.



by Vonda N. McIntyre

Vonda N. McIntrye, a US science fiction writer, is the author of the best-selling novel The Sun and the Moon, in which Louis XIV’s court philosopher has a love affair with a sea monster. Vonda makes her own hyperbolic sea monsters from glass embroidery beads.



by Aviva Alter

500 million years ago in what is known as the Cambrian Explosion life expanded from single-celled organisms into diverse multicellularity. In Aviva Alter’s polymorphous forms we also witness an explosive wealth of potential form.



The Beaded Reef began when Michigan resident Rebecca Peapples translated the techniques of hyperbolic crochet into beading. Rebecca’s work is Byzantine in style and miniature in scale, made from tiny glass embroidery beads. Rebecca follows the mathematics of hyperbolic structures precisely so her exquisite forms are geometrically perfect.



Sue Von Ohlsen owns a yarn store in Pennsylvannia and is another master beader. Sue specialises in the pseudoshere form, the hyperbolic equivalent of a cone. Where Rebecca uses mdele (sic) or herringbone stitch, which gives her pieces a striated look, Sue uses peyote stitch, a technique known to ancient cultures in Africa and the Americas.



Sarah Simons, who also made the doily animation in the Café, has invented a taxonomy of beaded kelps. Some of Sarah’s long thin pieces also resemble whelk egg cases. Many marine organisms – including whelks and nudibranchs – lay their eggs in long thin hyperbolic ribbons.


Christine Wertheim (Australia/CA), Margaret Wertheim (Australia/CA), Sarah Simons (CA), Evelyn Hardin (TX), Anna Mayer (CA), Helen Bernasconi (Australia), Marianne Midelburg (Australia), Barbara Wertheim (Australia), Helle Jorgensen (Australia), Ildiko Szabo (England), Heather McCarren (CA), Dr Axt (VT), Nancy Lewis (VT), Anitra Menning (CA), Shari Porter (CA), Vonda N. McIntyre (WA), Sue Von Ohlsen (PA), Rebecca Peapples (MI), Clare O’Callaghan (CA), Eleanor Kent (CA), Kathleen Greco (PA), Aviva Alter (IL), Nadia Severns (NY), Arlene Mintzer (NY), Jill Schrier (NY), Pamela Stiles (NY), Anita Bruce (UK), Mieko Fukuhara (Japan), with Ann Wertheim, Elizabeth Wertheim, Quoin, Allie Gerlach, Spring Pace, David Orozco, Karen Frazer, Karen Page, Lynn Latta, Diana Simons, Catherine Chandler, Sally Giles, Pate Conaway, Kristine Brandel, Cindy Bennish, Dagmar Frinta, Barbara Van Elsen, Njoya Angrum, Lily M. Chin, Siew Chu Kerk, Jessica Stapp, Kat Ramsland, Barbara Wakesfield, Amber Reyes, Barbara Robinson, Shirley Waxman, Ranu Mukherjee’s class at CCA, Katy Bevan, Rosy Sykes, Beverly Griffiths, Jane Canby, Jennifer White, Sharon Menges, Linda Shirey, Ellen Davis, Tane Clark, Nancy Yahrous.


Core Reef Assistant Curator: Anna Mayer.


The Latvian Reef was coordinated by Tija Viksna of Gallery Consentio in Riga.

The Latvian Schools Reef was co-led by Tija and Laila Strada of the Children’s Art School in Mazsalaca.


The Irish Reef was coordinated by Irene Lundgaard and Orla Breslin with contributions from Felt Makers Ireland.


All photos © The Institute For Figuring.

By Alyssa Gorelick, with Francine McDougall, Vincent Dachy, Margaret Wertheim, Christine Wertheim and Anna Mayer. Doillie images by Sarah Simons. “Reefer Madness” photo by Dr Axt.


Text by Margaret Wertheim.


The Crochet Reef Project has been generously assisted by grants from the Annenberg Foundation, the Andy Warhol Foundation for the Visual Arts and the Norton Family Foundation. With special thanks to Ren Weschler. When not crocheting corals, Christine Wertheim writes poetry and criticism and teaches in the School of Critical Studies at the California Institute of the Arts. Margaret Wertheim is a science journalist and communicator who writes books on the cultural history of physics. The Institute For Figuring is an organisation the sisters founded to enhance the public understanding of the poetic and aesthetic dimensions of science and mathematics. The IFF is based in Los Angeles and has a permanent address on the complex plane. For more information see