[2] From the perspective of the mathematical modeller, it is an emergent behaviour arising from simple rules that are followed by individuals and does not involve any central coordination.

[19] The concept of emergence—that the properties and functions found at a hierarchical level are not present and are irrelevant at the lower levels–is often a basic principle behind self-organizing systems.

Despite the lack of centralized decision making, ant colonies exhibit complex behaviours and have even been able to demonstrate the ability to solve geometric problems.

Yet put together, the cumulative effect of such behaviours can solve highly complex problems, such as locating the shortest route in a network of possible paths to a food source.

[70] The successful techniques used by ant colonies have been studied in computer science and robotics to produce distributed and fault-tolerant systems for solving problems.

This area of biomimetics has led to studies of ant locomotion, search engines that make use of "foraging trails", fault-tolerant storage and networking algorithms.

A new location is typically a kilometre or more from the original hive, though some species, e.g., Apis dorsata,[72] may establish new colonies within as little as 500 meters from the natal nest.

A good hive site has to be large enough to accommodate the swarm (about 15 litres in volume), has to be well-protected from the elements, receive an optimal amount of sunshine, be some height above the ground, have a small entrance and be capable of resisting ant infestation - that is why tree cavities are often selected.

In one case, researchers observed pink-striped oakworm moths (Anisota virginiensis) swarming at a carrion site, where decomposition likely increased soil nutrient levels and host plant quality.

[88][89][90][91] Notably, an innate predisposition to aggregate has been found in hatchlings of the desert locust, Schistocerca gregaria, independent of their parental phase.

The upwash assists each bird in supporting its own weight in flight, in the same way a glider can climb or maintain height indefinitely in rising air.

[104] The birds flying at the tips and at the front are rotated in a timely cyclical fashion to spread flight fatigue equally among the flock members.

In the case of foraging behaviour, captive shoals of golden shiner (a kind of minnow) are led by a small number of experienced individuals who knew when and where food was available.

This great migration, called the sardine run, creates spectacular feeding frenzies along the coastline as marine predators, such as dolphins, sharks and gannets attack the schools.

Most krill, small shrimp-like crustaceans, form large swarms, sometimes reaching densities of 10,000–60,000 individual animals per cubic metre.

Some species form surface swarms during the day for feeding and reproductive purposes even though such behaviour is dangerous because it makes them extremely vulnerable to predators.

The algorithm is based on three main factors: " (i) movement induced by the presence of other individuals (ii) foraging activity, and (iii) random diffusion.

Some copepods have extremely fast escape responses when a predator is sensed and can jump with high speed over a few millimetres (see animated image below).

In his 1800 book, Phytologia: or, The philosophy of agriculture and gardening, Erasmus Darwin wrote that plant growth resembled swarms observed elsewhere in nature.

[127] While he was referring to more broad observations of plant morphology, and was focused on both root and shoot behavior, recent research has supported this claim.

This is accomplished by growing in a direction that optimizes the distance between nearby roots, thereby increasing their chance of exploiting untapped nutrient reserves.

Additional inputs that inform swarm growth includes light and gravity, both of which are also monitored in the transition zone of a root's apex.

[129] These forces act to inform any number of growing "main" roots, which exhibit their own independent releases of inhibitory chemicals to establish appropriate spacing, thereby contributing to a swarm behavior pattern.

Myxobacteria swarm together in "wolf packs", actively moving using a process known as bacterial gliding and keeping together with the help of intercellular molecular signals.

Tim Burton's Batman Returns was the first movie to make use of swarm technology for rendering, realistically depicting the movements of a group of bats using the boids system.

A "swarm-moves" model was introduced by a Florida Institute of Technology researcher, which is appealing to supermarkets because it can "increase sales without the need to give people discounts."

Partially inspired by colonies of insects such as ants and bees, researchers are modelling the behaviour of swarms of thousands of tiny robots which together perform a useful task, such as finding something hidden, cleaning, or spying.

[155][156] In contrast macroscopic robots, colloidal particles at microscale can also be adopted as agents to perform collective behaviors to conduct tasks using mechanical and physical approaches, such as reconfigurable tornado-like microswarm[157] mimicking schooling fish,[158] hierarchical particle species[159] mimicking predating behavior of mammals, micro-object manipulation using a transformable microswarm.

Military swarming involves the use of a decentralized force against an opponent, in a manner that emphasizes mobility, communication, unit autonomy and coordination or synchronization.

In 2014 the U. S. Office of Naval Research released a video showing tests of a swarm of small autonomous drone attack boats that can steer and take coordinated offensive action as a group.