EXPLODE EVERY DAY: An Inquiry into the Phenomenon of Wonder
@ MASS MoCA, North Adams, MA
May 28, 2016 – February 28, 2017

Crochet Coral Reef
@ the University of California, Santa Cruz
February 10 – May 6, 2017


Crochet Coral Reef
@ Museum of Arts and Design, New York
September 15, 2016 – January 22, 2017

Night Begins the Day
@ the Contemporary Jewish Museum, San Francisco
June 18 – Sept 20, 2015

Crochet Coral Reef
@ Southwest School of Art, San Antonio, TX
February 12 – April 26, 2015

Crochet Coral Reef
@ New York University Abu Dhabi Institute, UAE
September 28 – December 5, 2014

making space
@ Google Venice Offices, Los Angeles
October 2013 – February 2014

Science + Art Residency:  Being Formed
@ Institute For Figuring, Los Angeles
July – December, 2013

An Alternative Guide to the Universe
@ Hayward Gallery, London
June 11 – August 26, 2013

Out of Fashion
@ GL Holtegaard Museum, Copenhagen
April 2013 – Jan 2014

making space
@ Institute For Figuring, Los Angeles
December 15, 2012 – June 29, 2013

Physics on the Fringe
@ Institute For Figuring, Los Angeles
April 14 – November 10, 2012

Mosely Snowflake Sponge Exhibition
@ The USC Libraries
September 20, 2012 – January 30, 2013

Midden Project
@ The New Children's Museum, San Diego, CA
October 15, 2011 –September 15, 2013

The Logic Alphabet of Shea Zellweger
@ The Museum of Jurassic Technology
Opening reception March 3, 2007 – March 3, 2012

@ The Walker Art Center
April 24 – September 29, 2009

Inventing Kindergarten
@ Art Center College of Design, Alyce de Roulet Williamson Gallery
October 13, 2006 – January 7, 2007

Hyperbolic Cactus Garden + Hyperbolic Kelp Garden
@ Fair Exhange, during the LA County Fair, Pomona Fairgrounds
September 8 – October 1, 2006

The Business Card Menger Sponge
@ Machine Project, Los Angeles
Los Angeles – August 26 – September 24, 2006

Crocheting the Hyperbolic Plane
@ Machine Project, Los Angeles
Los Angeles – July 2005

Philosophical Toys
@ Apex Art, New York
June/July 2005

Lithium Legs and Apocalyptic Photons
@ The Santa Monica Museum of Art
April 20 – June 9, 2002


Crochet Coral Reef Exhibitions

Hyperbolic: Reefs, Rubbish, and Reason
@ The Williamson Gallery, Art Center College of Design, Pasadena, CA
June 6 – August 21, 2011

Crochet Reef
@ The Smithsonian's National Museum of Natural History, Washington, DC
October 16, 2010 – April 24, 2011

Crochet Reef
@ The Science Gallery, Dublin
March 20, 2010 – June 11, 2010

The IFF "Bleached Reef"
@ The National Design Triennial at the Cooper-Hewitt, NYC
May 14, 2010 – January 9, 2011

Crochet Cactus Garden
Jackson Hole, WY
June 26 – September 28, 2009

Crochet Reef
Scottsdale, AZ
April 11 – July 11, 2009

Crochet Reef Show
@ Track 16 in Los Angeles
Jan 10 – Feb 28, 2009

New York and Chicago Reefs
Staten Island
Sept 27 – Dec 20, 2008

UK Reef Tour
Autumn 2008

Plastic Exploding Inevitable Reef
San Francisco
Sept 7 – Oct 3, 2008

Crochet Reef Symposium
@ Southbank Center
Friday June 13, 2008

Crochet Reef
June 11 – August 17, 2008

Crochet Reef
New York
April 6 – May 18, 2008

The Crochet Cactus Garden
@ The Wignall Museum, Chaffey College
January 29 – March 1, 2008

The Crochet Cactus Garden
@ The David Weinberg Gallery
October 26 – December 29, 2007

The Crochet Coral Reef
@ The Chicago Cultural Center
October 13 – December 16, 2007

The Crochet Coral Reef
@ The Andy Warhol Museum
March 11 – June 17, 2007



at the Institute For Figuring in Los Angeles

Exhibition Dates: December 15, 2012 – June 29, 2013
Opening Reception: Saturday December 15, 2012

Making Space exhibition at the IFF. December 2012. Photo © IFF Archive.

Space has become a central subject of our time. Astronomers are exploring the far reaches of outer space, probing the birth of our universe; physicists propose that we live in a 10- or 11-dimensional hyperspace and mathematicians are discovering new kinds of geometric and algebraic spaces. Meanwhile, GPS systems help us to navigate urban space, Google Maps allow us to explore geographical space, and spatial representations of data have become critical in fields as diverse as pharmaceutical research and weather prediction. Such tools change the way we understand our world and lead to new ways of solving problems. making space offers a multifaceted exploration of what we mean by the word “space” in its many diverse manifestations, historically and today.

Accompanying this exhibition is a series of lectures, workshops and conversations. In lectures we’ll examine how the modern scientific conception of space evolved as the science of physics matured. What does it mean to say that something has two, three, or ten spatial dimensions? What does relativity tell us about the architecture of space? How do string theorists think about “brane-space”? We’ll also look to artists, writers and mathematicians as we host conversations about visual space, literary space and phase space.

In workshops, visitors will have the chance to construct spatial forms of their own. Hyperbolic planes made from paper strips, platonic solids woven from bamboo sticks, pleated parabaloids and graph-paper tessellations; in each case audiences can engage with key spatial ideas though activities that are at once playful and pedagogically rich.

If you feel like playing, have a seat and fold some of our 60,000 specially designed business cards. Over the next six months we’ll be using them to create geometric, fractal-inspired sculptures. You can design new shapes yourself. The project is an exercise in applied mathematics and participatory aesthetic practice. What happens when art and geometry combine? We invite you to join us in exploring this boundary and in developing a new landscape of form.

This installation continues from December 2012 through May 2013.

Christina Simons installs Making Space exhibition at the IFF. December 2012. Photo © IFF Archive..

Business Card Fractal Sculptures

The IFF’s business card sculpture project has been inspired by the work of Dr. Jeannine Mosely, an MIT trained engineer and pioneer of business card origami. Dr. Mosely developed her methods as a means to construct models of fractals, geometric objects with intermediate dimensionality. Taking Dr. Mosely’s techniques as our starting point, the IFF and its collaborators are developing an ecology of fractal-like forms. This is an on-going experiment: We invite your input. Feel free to add to the structures on display here, to play with the shapes as shown and adapt the techniques described, or develop new pieces of your own.

Our metaphor here is the evolution of life. Scottish chemist  Graham Cairns-Smith has theorized that in the pre-biotic world life catalyzed itself on the crystalline substrate of clays. Complex, self-replicating compounds, clays hold within themselves an intriguing language of form. Somewhere around 3.7 billion years ago, the inorganic geosphere transformed into a zoosphere as the first organisms swirled into being. How did this transition from geo to bio occur?

Cairns-Smith is not the only thinker who has proposed that the structure of crystals played a role in the emergence of life. For Friedrich Froebel, founder of the kindergarten movement, complexification was intrinsically a movement from the simple geometry of regular crystals - the cubic lattice of salt, for example - to ever more complicated assemblies. Along with other Goetherian philosophers, Froebel saw the evolution of form as perhaps the fundamental question of science.

Following on from the success of the Institute’s Crochet Coral Reef project (begun in 2005), with this exhibition we again offer an open-ended exercise in participatory form-making. Join us in developing a business card origami fractal “tree of life.”

exhibition design: Margaret Wertheim
core card folders: David Orozco, Christina Simons, Tracy Tynan, Oscar Collins, Margaret + Christine Wertheim
card design: Margaret Wertheim + Cindi Kusuda
assistant curators: Anna Mayer + Jemima Wyman

Tessellation Chapel

Across the globe, humans have been fascinated by the ways in which a plane can be tiled or tessellated. Deriving from the Latin word tessella – a small cubical piece of stone or glass used for making mosaics – a tessellation is any pattern that fills the plane completely without gaps. Naturally occurring tessellations include the hexagonal structure of honeycombs and the hexagonal fracturing of rock that forms as lava cools in places such as the Giant’s Causeway in Northern Ireland.

In 1618 the mathematician Johannes Kepler wrote one of the first treatises on regular and semi-regular tessellations. Three centuries later, in 1891, the Russian crystallographer E.S. Fedorov proved that every periodic tiling of a plane is one of 17 basic types, known as the “wallpaper groups”. Fedorov’s work is seen as the beginning of the mathematical study of tessellations, which is today a hugely dynamic field of research with application to areas of science and technology as diverse as the creation of new materials, cryptography, sheet metal cutting, quantum mechanics, data compression and CGI animation.

Only three types of regular tessellations exist: those made up of hexagons, squares, and equilateral triangles. A semi-regular tessellation uses two or more regular polygons and every vertex point is the same; there are eight of these types. Other varieties include irregular, periodic, aperiodic, asymmetric and fractal tessellations. Research now extends to tessellations in higher-dimensional and non-Euclidean spaces. The types of tessellation possible in a space are one way of characterizing the space itself.

Artists and craftspeople of many cultures have incorporated tessellations into their designs. The embroidered pieces on display here are traditional works made by women of the Hmong, from the mountainous regions of China, Vietnam, Laos and Thailand. On the video monitor are tessellation patterns underlying Islamic mosaics from the Alhambra Palace in Spain and other Muslim architectural wonders. These tilings, made between the 8th and 14th centuries, are still revealing secrets to mathematicians today.

exhibit curator: Christine Wertheim

Islamic Mosaics

In the classical Islamic world, teams of master craftsmen covered the walls of mosques and palaces with tessellations of dazzling complexity. Multi-pointed stars, often exhibiting 8-fold and 64-fold symmetry, were a favored motif that arose soon after the birth of Islam and quickly spread outward across the Middle East, into Northern Africa and Western Europe. Artisans would carve these designs in wood or stone, build them into latticework, or assemble them from baked terracotta tiles, a style known as Zellij.

All 17 of the possible wallpaper groups, each representing a mathematically distinct pattern, were used by Islamic mosaicists and by ancient Egyptian craftsmen. Designs were often family secrets passed down from father to son. The images on display here are taken from the book Arabesques: Decorative Art in Morocco by Jean-Marc Castera, who has mapped the patterns underlying many Moroccan mosaics and murquanas. These three-dimensional tessellated structures, made from carved blocks of wood, resemble stalactites and were used to adorn ceilings.

It is now known that in the Middle Ages Islamic mosaicists also discovered aperiodic tiling. Western mathematicians long believed such patterns were impossible and discovered them only in the 1960’s. An aperiodic tiling does not repeat itself on any scale and appears at once regular and irregular. Astoundingly, such patterns are present in the structures of quasicrystals, exotic compounds with symmetries that can be understood as projections of regular structures in higher-dimensional space. In 2011, Israeli scientist Daniel Shechtman was awarded the Nobel Prize in chemistry for discovering quasicrystals, after years of ridicule from colleagues. “There are no quasicrystals,” said the great Linus Pauling, “only quasi-scientists.” The Nobel Committee described these materials as “fascinating mosaics of the Arab world reproduced at the level of atoms.”