In this circle we investigated something called the “falling sand pile”. But sand is boring, so instead we studied falling chickens! The primary rule of falling chickens is
When 4 chickens land in someone's backyard, they "break out" and go to the neighbors' yards instead.
In the process we discovered a new sequence: When the chickens fall on one square in the middle of the grid, how long does it take for the chicken fractal to spread n units up from the center? Our answer so far:
1, 4, 16, 44, 88, 144, 208, 320, 408, 512, 672, 788, 948, 1096, 1288, 1552.
We have yet to analyze the pattern.
Here is the game and questions
How Many Backyards?
Click on the Yards to Add Chickens
Or Make It "Rain Chickens":
|0 chickens||1 chickens||2 chickens||3 chickens|
|Number of Yards||0||0||0||0|
- 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?
In addition, we thank Marcel Salathé for a nice outline of the code to implement the “chicken rule”.