Birds on a field

How many birds could potentially fit on a wire? Well it depends on how "jumpy" they are. In [1] it was shown that density of birds is approximately $\frac{1}{2r+1}$ in the steady state regime (here $r$ is the tolerance distance of the birds). In this post we provide an interactive applet for the two dimensional case (field).

Interactive app

This interactive app visualizes a finite discrete field (there are 50x40 spots for the birds to land on). Empty spots are shown in grass green (to imitate the field) or red (if the spot was recently vacated), while spots taken are shown in dark gray (most "crow-like" color).

As in the previous app we also plot the time evolution of the fraction (density) of birds on the field.

In this particular app we have assumed circular neighborhood around the arriving bird. Namely bird $j$ flies away if

$$\begin{array}{}\text{(1)}& \sqrt{(x_j-x{)}^2+(y_j-y{)}^2}\le r.\end{array}$$

In the above $(x,y)$ are the coordinates of recently landed bird.

References

• P. L. Krapivsky, S. Redner. Birds on a Wire. arXiv:2205.00995 [cond-mat.stat-mech].