Look, coral reefs, made from yarn. Aren’t they beautiful? This is one of a dozen or so troughs of subnauticalia on show at the Hayward Gallery from today.
The ‘hyperbolic crocheted coral reef’ is the creation of the Institute for Figuring, a curiously named sci-art outfit from Los Angeles. They’ve exhibited the reefs in several US cities, and now bring their hyperbolic handicrafts to London.
Why hyperbolic? It’s a curious tale, this. I don’t profess to understand the maths of three-dimensional surfaces, but apparently there are three types of geometry: the good old Euclidian system of planes, angles and parallel lines; spherical geometry; and hyperbolic geometry in which the surface curves away from itself from any given point (kind of the opposite to a sphere where the surface curves in on itself). Or something. Any mathematicians reading this, please correct me.
Such a surface eluded simple physical modelling until 1997, when someone figured out a way to do this, implausibly, through the ancient art of crochet (like knitting, but with a single hooked-needle). Here’s a fuller account of this wonderful yarn, which I don’t quite buy (why not just mold the structures out of wax or something?).
Turns out that nature (not Nature) is an old hand at bypassing Mr Euclid. Corals have grown into hyperbolic structures for millions of years. The new exhibition recreates these glorious geometries from thread, with sparing use of beads, plastic ties and other items of haberdashery. The main display is free to view in the Haywood, but other examples can be found inside the Royal Festival Hall until mid-August. Highly recommended.
Two of my friends (including one NN bod! ) submitted corals for this, so I’m going coral spotting soon. I’m wishing I had now…
And it’s too late to talk hyperbolic geometry, but essentially, hyperbolic geometry differs from Euclidian “everyday” geometry because hyperbolic geometry breaks the Parallel Postulate. This means that, whereas on this computer screen this line – can only have one parallel line = in hyperbolic space, it can have loads. Which is fun.
As I understand it, the reason crochet is useful to understand this, is that the stitches are all the “same” and “flat” but draw lines and surfaces that appear to us to be curved. Though to be sure, I’d have to swot up on lots more maths, or just ask Madeleine when I see her on Saturday…
s that the stitches are all the “same” and “flat”
OK, a slightly better phrasing of that is that you can view each stitch as an individual point on the surface.
(Is it bad that that was my waking thought?)
Excellent, thanks Scott.
or just ask Madeleine when I see her on Saturday
Hey, why not point her to this post and see if she’ll comment? It’d be nice to get an expert viewpoint.
Will do! As soon as she is near a computer, I’ll get her to post :)
Hello Matt and Scott,
Here I am, almost as soon as I got near to a computer but I had to comment on Scott’s triumph with the cakes first!
Anyway, I’m not sure which part of the Cabinet Magazine article you don’t buy, Matt, so I may be answering the wrong point but here goes.
There are a couple of things to consider about making models of hyperbolic planes in wax. Firstly you have to visualise what you’re making before you make it. In these days of Mathematica and rapid prototypers it’s not such an issue though. See George Hart’s page or Bathsheba Sculpture for instance
However with crochet you can set up an algorithm to generate the surface before you know what it looks like. Think cellular automata. You define a starting position and a rule for the rate of curvature and away you go. Thinking about it this way gives you a way into how it plants and animals sometimes grow these shapes. Each layer of cells (bio or digital) is generated from the ones that went before. Some of this thinking goes back to the great Scottish polymath D’arcy Wentworth Thompson
Secondly a wax or plaster model is quite rigid but a fabric one is flexible and lets you explore different embeddings of a plane in 3D. You can make models of these structures from paper but they’re very fragile. Daina Taimina had inherited paper models from her predecessor when she took up a particular post. The models were made of little strips all glued together. You could do the same with fabric but the CAs side to knitting and crochet give an added insight and a lot more control over the finished item.
Hope that’s helpful – better get on with the day job now.