Busy beaver

Even a simple Turing Machine can have a surprisingly complicated 
behavior:

A _ B X R
A X C _ L
B _ A X L
B X A _ R
C _ D _ L
C X Z X R
D _ E X R
D X D X L
E _ F _ L
E X E _ L
F _ F X R
F X B _ L

It's easy to manufacture a machine that can write an infinite number of 
X'es, and which never halts:

	A _ A X R

but that's not complicated behavior; it's simple.

The six-state machine above is complicated.  Given a blank tape, does 
eventually halt, but only after 95,547,257,425,490 steps.