Julia's Fractals

The latent mathmo in me loves ferns for more than just their delicate nature, ease of care and ability to spread to fill almost any space. I'm a big fan of fractals ("a rough or fragmented geometric shape that can be subdivided into parts, each of which is (at least approximately) a reduced-size copy of the whole"). I'm especially taken with Julia fractals:



And fractals are around in nature - the head of a romanesco broccoli (or indeed any other kind of broccoli or cauliflower), the branches of a tree, feathers - and of course fern fronds.



Ferns are not exact fractals, but the individual leaves do resemble the fronds as a whole. I love my shuttlecock fern, Matteuccia struthiopteris, and it's chucking out runners pretty quickly. I hacked one off to give to a friend three weeks ago, and a forumer has just mentioned that he'd love one. So it looks like it's in with the secateurs again tonight! Fortunately, shuttlecocks are pretty sturdy, and while I should probably have taken all the runners off in one go (if I was going to), it shouldn't hurt it at this stage. Nothing a good dose of mycorrhizal fungi won't fix anyway.

Sitting outside contemplating my ferns, I was reminded of two variations on a rhyme I was taught at university:

Big whorls have little whorls that feed on their velocity,
And little whorls have lesser whorls and so on to viscosity.

and its inspiration:

Big fleas have little fleas upon their backs to bite them
And little fleas have lesser fleas, and so ad infinitum.

I wonder if there's a version about fronds. I'm no poet, otherwise I'd try to come up with one myself.