LOGO Challenge - Circles as Animals

At the school next door, two girls had been working on circle problems...

They had gone on to use circles to represent cellular growth in some science they had been doing. They had been looking at how cells grow, in particular those that grew under certain rules that repeat!

Look for yourself and see if you can anticipate successive 'generations' of the two animals shown here.

More importantly can you construct elegant procedures to draw them out?

Here is the first 'animal'.

An interesting thing about the second 'animal' is that it is always unicursal, that is you can trace the 'animal' going over each line once and once only, eventually returning to the original starting point.

And another

Can you design cellular animals of your own that are also unicursal?

Finally, a representation of the old mathematical chestnut of squaring the circle, which you might like to research and consider.