Tuesday, May 12, 2009

The Chaos Game

The Chaos Game can be played here. http://math.bu.edu/DYSYS/applets/chaos-game.html
I was asked to find an algorithm to solve the game. This post shows that with one initial choice of your original 3 moves, solving the game can be very easy be repeating a simple process until solved. I don't understand why the first 3 moves are what they are I just found the pattern based on observation.


How to beat the Chaos Game on Master
• First find your target (it can be hard on master)
• Focus looking at it on it’s first level














•Moves 1,2 and 3: The target is on the right triangle, so we move Blue, Red, Green(Note: If the target was on the top triangle we would have moved Blue, Red, Red.
If the target was on the left triangle we would have moved Red, Blue, Blue.)
This is the only unique step, all the other steps now follow a pattern.
• Now we zoom out our focus and look at the next level


• Move 4: As you can see the target is now in the top triangle in our new focus area. Making our next move to be Red. The next steps are just a repetition of this zooming out and seeing what triangle our target is in.




• Move 5: In this new focus our target is in the right triangle so our next move is Green.



• Move 6: Again in this focus we the target in the right triangle so we move Green.



• Move 7: Now in our final step we focus on the entire object. Our target is in the top triangle so our final step is to move Red.



This method can be used to solve The Chaos game on any level!!!

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