There’s a great post up on The Atavism by David Winter where he explains why the shape of the snail’s shell is a logarithmic spiral. What I find interesting is that the shell has the logarithmic spiral shape under two assumptions:

The radius of the shell increases exponentially as the snail ages (i.e., the rate of radial growth is proportional to the shell radius) and,

The angle between the centre of the snail and the end of the shell changes at a constant rate – like the second hand of a clock which moves at a constant rate of 360-degrees per minute.

Does anyone know what kind of snail this is? Photo credit: Robyn Hurford

I was hoping that we could use this simple model to do a couple of quick experiments.

Firstly, can we validate the hypothesis that snail shells are logarithmic spirals using something like a Turing test?

That is, among a set of spirals are blog-readers going to pick out the logarithmic spiral as being snail-like?

Secondly, since the art of model derivation is subjective, I want to solicit opinions on this particular model derivation – to see if everyone has the same instinctive appraisal of model assumptions or if there are a range of different tastes on the matter.

… and after you’ve voted be sure to go check out The Atavism for a nice explanation and some great snail pictures!

One thought on “Snails shells: the logarithmic spiral”

The snail belongs to the Powelliphanta group of snails. It is found in Kahuranga National Park, Tasman NZ. It is a carnivorvous land snail that lives on the native worms of the region.

The snail belongs to the Powelliphanta group of snails. It is found in Kahuranga National Park, Tasman NZ. It is a carnivorvous land snail that lives on the native worms of the region.