The Hyperbolic Crochet Coral Reef is a worldwide project created by Margaret and Christine Wertheim of the Institute for Figuring in Los Angeles.
The Sydney Hyperbolic Crochet Coral Reef was on display during 21-30 August in the Powerhouse Museum, 500 Harris Street, Ultimo. Fortunately I was in Sydney last week and saw it first hand. Here's some of my photos of the exhibition.
The Reef begins with the technique of hyperbolic crochet discovered by Dr. Daina Taimina. In 1997, Daina Taimina, a mathematician at Cornell University, crocheted a physical model of hyperbolic space. Visit http://theiff.org/oexhibits/oe1e.html to read more about Daina's crochet models.
You can crochet your own hyperbolic plane by increasing incrementally. All you have to remember is to increase every nth stitch each row. For example, if n=4 you increase every 4th stitch, every row. As you increase, the surface begins to ruffle naturally. An article in Interweave Crochet magazine gives you the complete instructions at http://theiff.org/press/interweave.html.