A cluster of glowing dots drifts through the darkness, now compressing into islands, now spreading out in waves. These are not fish or birds: this is a mathematical model of active matter, where each particle spends its own energy on movement, and also is born, dies, and competes with neighbors for space.
The authors of the new study started from the microworld: each particle follows simple random rules — a push, a turn, a division, or a disappearance. From this chaos, they derived equations for the entire cloud of such particles, as if describing a crowd not through each individual, but through density and overall flow. The key trick is a special mathematical approach (the von Mises approximation), which allowed them to close the chain of equations and obtain a working hydrodynamics of reproducing active matter.
The theory was immediately tested on a concrete example — the "Active Brownian bugs" model. The calculations predicted two types of instabilities: one gives rise to stationary clumps (like bacterial colonies on a Petri dish), the other to traveling swarms. Computer simulations confirmed: depending on the settings, the system transitions from a uniform "soup" to striped patterns or groups that move through space as a single entity.
This approach is not just abstract theory. It provides a common language for describing a wide range of living and quasi-living systems: from biofilms and tumor cells to swarming robots. And the key to order here is not an external conductor, but the internal rhythm of birth and death.
In the "Active Brownian bugs" model, particles have no memory and do not communicate with each other: their entire "social life" boils down to taking up space and occasionally disappearing, freeing it for offspring.
The swarms of self-replicating nanomachines in Michael Crichton's novel "Prey" are a pure example of active matter whose behavior is described by such equations.