Falling Chickens

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.