The Sierpinski Triangle "Chaos Game" Challenge
How to play the "Chaos Game" challenge. The game board below consists of the Sierpinski gasket drawn at level 2, i.e., after two iterations with nine smaller triangles. One of these triangles is colored green; this is the Target. You also see a point colored red at one of the numbered corners of the triangle. This is the Seed. Your goal is to move the Seed into the interior of the Target in as few moves as possible. Each time you make a "move" in the game, this point will move to a new location in the game board. This becomes your current location. Both the Target and the Seed are chosen at random each time you start a new game.
There are three possible moves. When you click on the button at one of the vertices, your current location moves half the distance to that vertex. By a judicious choice of moves, you should be able to get your point into the interior of the Target in the minimum number of moves (e.g. 4 moves in the "Easy" case of level 2 [Minimum Moves Details]). This is indicated as the goal in the left sidebar. Your score (the number of moves you have made) is also recorded in the sidebar window. When you succeed in moving your current location into the interior of the Target, you receive a message telling you so.
More difficult Targets. If you select Medium (level 3), Hard (level 4), or Master (level 5) in the "Level" dropdown menu, the Target will be chosen at deeper levels of the Sierpinski gasket. The goal in the sidebar is adjusted accordingly.
Can you find an algorithm that will always move the Seed into the Target in the minimum number of moves, no matter the level? Give it a try!
| Other chaos game challenges involving rotations | |||
|---|---|---|---|
| 0 Rotations | 1 Rotation | 2 Rotations | 3 Rotations |
|
 |
 |
 |
| Current Challenge |
Play | Play | Play |
Credit: Based on the original Java game (1995) created by Bob Devaney and students at Boston University using an idea of Kevin Lee at St. Catherine University.
