When 4 chickens land in someone’s backyard, they “break out” and go to the neighbors’ yards instead.

#### How Many Backyards?

Click on the Yards to Add Chickens

#### Or Make It “Rain Chickens”:

#### Sound Effects?

0 chickens | 1 chickens | 2 chickens | 3 chickens | |
---|---|---|---|---|

Number of Yards | 0 | 0 | 0 | 0 |

## Math Questions

- If one of the yards has 2 or more chickens, is it possible to go back to all yards having less than 2 chickens?
- Does the order at which chickens arrive change the result? (or just the locations where they arrive)
- How many falling chickens does it take for the locations to stop changing so much?
- If chickens always fall in the same spot, how does the total number of chickens relate to the “range” of the chickens?
- What percentage of yards end up with 0, 1, 2, or 3 chickens?
- Is it possible to add enough chickens to the middle of the neighborhood to result in no chickens in the middle?
- Does it matter whether chickens arrive in the “middle” of the neighborhood (versus the yards near the edges)?
- What happens if you add chickens to one yard every time?
- What happens if you alternate adding chickens between two yards?
- Which is better, spreading the chickens out in a consistent way, or letting them fall randomly?

## Resources

This activity is an exploration of a class mathematical objects called abelian sandpiles. We highly recommend reading Jordan Ellenberg’s wonderful article about sandpiles.

In addition, we thank Marcel Salathé for a nice outline of the code to implement the “chicken rule”.