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## 'LOGO Challenge - Circles as Animals' printed from http://nrich.maths.org/

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.