Hi Dennis,
the math of a spiral is as easy as you wish it to be - but in polar coordinates
The simplest one is (rho) = a (theta) [ sorry, can't manage Greek letters here], a docile and tame linear spiral also known as Archimede's.
Then there's the one used by snails, looking like (rho) = exp (k (theta)): the larger the animal, the faster it grows - at least until it meets a hungry Frenchman.
If you want to make the latter more realistic you might as well consider that an element of cross-section has anyway to accommodate only a slice of the animal, thus make it (rho) = exp (k (theta)) ^ (2/3) [one dimension falls off].
However if you want it really complicated and interesting, the only limit is your fantasy. Unless you're married, of course - then the first unobjectionable obstacle would be your wife
