In the case of directed propulsion, which is driven by a chemical gradient, this is referred to as chemotaxis, observed in biological systems, e.g. bacteria quorum sensing and ant pheromone detection, and in synthetic systems, e.g. enzyme molecule chemotaxis[3] and enzyme powered hard and soft particles.

These collective behaviours mimic the self-organization observed with the flocking of birds, the swarming of bugs, the formation of sheep herds, etc.

The most prominent examples of collective behaviours in these systems are fish schools, birds flocks, sheep herds, human crowds.

[7] Further, it has been shown that they will preferentially move towards a region of higher substrate concentration,[8][9] a phenomenon that has been developed into a purification technique to isolate live enzymes.

For instance, the two sides of the Janus particle can induce a local gradient of, temperature, electric field, or concentration of chemical species.

[28][29] In 2021, it was experimentally shown that completely symmetric particles (spherical microswimmers in this case) experience a net thermophoretic force when illuminated from a given direction.

These quasi-particles demonstrate a surprising behaviour: In response to an external load they move with a constant velocity proportional to the applied force, just as objects in viscous media.

[35] The prominent and most spectacular emergent large scale behaviour observed in assemblies of SPP is directed collective motion.

Another class of large scale behaviour, which does not imply directed motion is either the spontaneous formation of clusters or the separation in a gas-like and a liquid-like phase, an unexpected phenomenon when the SPP have purely repulsive interaction.

[38][39]Simulations demonstrate that a suitable "nearest neighbour rule" eventually results in all the particles swarming together or moving in the same direction.

[41] On-lattice models such as BIO-LGCA models have been used to study physical aspects of self-propelled particle systems (such as phase transitions and pattern-forming potential[42]) as well as specific questions related to real active matter systems (for example, identifying the underlying biological processes involved in tumor invasion[43]).

[1] In the field, according to the Food and Agriculture Organization of the United Nations, the average density of marching bands is 50 locusts/m2 (50 million locusts/km2), with a typical range from 20 to 120 locusts/m2.

[45]: 29  The research findings discussed above demonstrate the dynamic instability that is present at the lower locust densities typical in the field, where marching groups randomly switch direction without any external perturbation.

Understanding this phenomenon, together with the switch to fully coordinated marching at higher densities, is essential if the swarming of desert locusts is to be controlled.

Such state switches can occur with astonishing speed and synchronicity, as though all the members in the group made a unanimous decision at the same moment.

As a paradigm, they considered how flying birds arrive at a collective decision to make a sudden and synchronised change to land.

[49] "Our main motivation was to better understand something which is puzzling and out there in nature, especially in cases involving the stopping or starting of a collective behavioural pattern in a group of people or animals ... We propose a simple model for a system whose members have the tendency to follow the others both in space and in their state of mind concerning a decision about stopping an activity.

"[47] The model could also be applied to a swarm of unmanned drones, to initiate the desired motion in a crowd of people, or to interpreting group patterns when stock market shares are bought or sold.