A Game of Life: Microorganism Billiards

The angle of incidence is strongly related to the angle of “reflection” in this new real-AND-SIMULTANEOUSLY-artificial game of the mathematical gods:

Microorganism Billiards,” Colin Wahl, Joseph Lukasik, Saverio E. Spagnolie, Jean-Luc Thiffeault, arXiv 1502.01478, February 5, 2015. (Thanks to Mason Porter for bringing this to our attention.) The authors, at the University of Wisconsin, report:

“Recent experiments and numerical simulations have shown that certain types of microorganisms “reflect” off of a flat surface at a critical angle of departure, independent of the angle of incidence. The nature of the reflection may be active (cell and flagellar contact with the surface) or passive (hydrodynamic) interactions. We explore the billiard-like motion of such a body inside a regular polygon and show that the dynamics can settle on a stable periodic orbit, or can be chaotic, depending on the swimmer’s departure angle and the domain geometry. The dynamics are often found to be robust to the introduction of weak random fluctuations. The Lyapunov exponent of swimmer trajectories can be positive or negative, can have extremal values, and can have discontinuities depending on the degree of the polygon. A passive sorting device is proposed that traps swimmers of different departure angles into separate bins. We also study the external problem of a microorganism swimming in a patterned environment of square obstacles, where the departure angle dictates the possibility of trapping or diffusive trajectories.”

Here’s further detail from the study:

billiards detail

BONUS: That’s a game of life. It’s different, mostly, from THE game of life. THE game of life is John Conway‘s “The Game of Life“:

For most of the world, the main introduction to Conway’s Game of Life was Martin Gardner’s 1970 article in Scientific American.