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When a turtle update operation cannot finish because the underlying canvas has been cleared (when the STOP button is pushed), turtle.Terminator is raised. When turtledemo runs the main function of a demo, it catches any Termininator raised before main returns. 
However, special demos leave an event loop running after main returns. If the demo is free running, as with clock and minimal_hanoi, clicking STOP causes such exceptions. (This is not be a problem with paint as updates only happen in response to mouse events on the canvas and complete before a user could move the mouse to the STOP button.)
This is the clock trackback, with common file prefix removed:
 \tkinter\__init__.py", line 1487, in __call__
 return self.func(*args)
 \tkinter\__init__.py", line 532, in callit
 func(*args)
 \turtledemo\clock.py", line 116, in tick
 second_hand.setheading(6*sekunde)
 \turtle.py", line 1935, in setheading
 self._rotate(angle)
 \turtle.py", line 3277, in _rotate
 self._update()
 \turtle.py", line 2659, in _update
 self._update_data()
 \turtle.py", line 2645, in _update_data
 self.screen._incrementudc()
 \turtle.py", line 1291, in _incrementudc
 raise Terminator
The hanoi traceback starts differently:
 \tkinter\__init__.py", line 1487, in __call__
 return self.func(*args)
 \turtle.py", line 686, in eventfun
 fun()
 \turtledemo\minimal_hanoi.py", line 53, in play
 hanoi(6, t1, t2, t3)
 ...<5 recursive calls deleted>
 \turtledemo\minimal_hanoi.py", line 36, in push
 to_.push(from_.pop())
 \turtledemo\minimal_hanoi.py", line 36, in push
 d.setx(self.x)
 \turtle.py", line 1807, in setx
 self._goto(Vec2D(x, self._position[1]))
 \turtle.py", line 3178, in _goto
 <last 3 lines as above>
These exceptions and tracebacks do not stop the master demo window, but are printed to the console (python -m turtledemo) or Idle Shell (open in editor, run). They are ugly, might unnecessarily alarm a naive user, or falsely teach that tracebacks are to be ignored.
In the patch to clock.tick, I put try: at the top, to be safe, although just before the update of the second hand might be good enough.

New changeset a43d03cdf38b by Terry Jan Reedy in branch '2.7':
Issue #21823: Catch turtle.Terminator exceptions in turtledemo.
http://hg.python.org/cpython/rev/a43d03cdf38b
New changeset 1ae2382417dc by Terry Jan Reedy in branch '3.4':
Issue #21823: Catch turtle.Terminator exceptions in turtledemo.
http://hg.python.org/cpython/rev/1ae2382417dc 

In 2.7, the exception in tick occurred at tracer(False), so I moved try: up in all patches.

Since hanoi do not have user interaction, once started, it does not need to be 'special'. Like planets_and_moon, it could run until done and then return 'Done'.