The Chaos Game: Hint

Here's a sequence of moves (W,N,W,E,N) that moves the bug into the triangle in 5 turns.

Here's a sequence of moves (W,N,E,N) that moves the bug into the triangle in only 4 turns.

Try designating different triangles as your goal and finding the fastest path to them. You'll discover that the best path always takes 4 moves.

If you need another hint, you can mail me at fields@SouthernCT.edu