Predicting when and how collections of particles, robots, or animals become orderly remains a challenge across science and engineering.
In the 19th century, scientists and engineers developed the discipline of statistical mechanics, which predicts how groups of simple particles transition between order and disorder, as when a collection of randomly colliding atoms freezes to form a uniform crystal lattice.
More challenging to predict are the collective behaviors that can be achieved when the particles become more complicated, such that they can move under their own power. This type of system — observed in bird flocks, bacterial colonies and robot swarms …
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