Friday, 5 October 2012

Toral Communities

In dynamical systems, a wild torus is an invariant torus whose cross-section is a nowhere differentiable closed curve. The picture above, taken earlier this summer, is rather different: it is a torus in the wild. I noticed some last year, but wasn't able to get a good photo. They returned this year and the light was better, but even so I have had to enhance the contrast to make the torus clearer.

Tori in nature are usually either somewhat contrived (humans, earthworms, ...) or the result of a complicated extrusion process (smoke rings). This, I believe, is a community of simple cellular organisms that has formed a natural torus. For a while I thought it must be an egg-containing jelly (extrusions again) but a bit of research on the web makes me think it is much more likely to be a jelly-like community that can create columns, and the ends of the cylinder have joined to form a torus.

Why would this be beneficial? Perhaps it is a mechanism to limit further growth or recruitment. The active area of a cylinder is likely to be the ends, so closing in on itself like this could be a way of preventing further organisms from joining. A gated toral community! If the column becomes too large it might be more easily torn or snagged on other objects, so some limitation on size might be necessary.

Fairy rings (holes in the growth of a clump of plants) may also be toral in nature, extending below the surface. But here I think the mechanism is different -- either nutrients in the central region have already been used up, or dying plants leave behind a chemical residue that prevents new growth in that region. Of course the reason the latter mechanism is beneficial might be due to the former suggestion.
On the subject of natural tori, I seem to remember Bilbo and Gandalf engaging in a smoke ring competition in Lord of the Rings (The Fellowship of the Ring). Ah yes, here's a CGI version!