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Emergence is the process of deriving some new and coherent structures, patterns and properties in a complex system. Emergent phenomena occur due to the pattern of interactions between the elements of a system over time. Emergent phenomena are often unexpected, nontrivial results of relatively simple interactions of relatively simple components. What distinguishes a complex system from a merely complicated one is that some behaviours and patterns emerge in complex systems as a result of the patterns of relationship between the elements.
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An emergent behaviour or emergent property is shown when a number of simple entities (agents) operate in an environment, forming more complex behaviours as a collective. A system made of several things can host properties which the things themselves do not have. For instance, consider two points on a plane. These points will have a distance between them. This distance is not itself a property, but exists in the relation between the points. Emergent properties can arise not only between things in the system, but between other emergent properties. The number and subtlety of these properties can be very much greater than the number of things.
Emergent properties arise when a complex system reaches a combined threshold of diversity, organisation, and connectivity. The property itself is often unpredictable and unprecedented, and represents a new level of the system's evolution. The complex behaviour or properties are not a property of any single such entity, nor can they easily be predicted or deduced from behaviour in the lower-level entities. The shape and behaviour of a flock of birds or school of fish are readily understandable examples, and it is typical that the mechanisms governing the flock or school are harder to grasp than the behaviour of individual birds or fish.
This helps to explain why, for instance, the number of ways of packing boxes into a truck increases exponentially with the number of boxes and why the fallacy of division is a fallacy. According to an emergent perspective, intelligence emerges from the connections between neurons, and from this perspective it is not necessary to propose a "soul" to account for the fact that brains can be intelligent, even though the individual neurons of which they are made are not.
Emergent behavior is also important in games and game design. For example, the game of poker, especially in no limit forms without a rigid betting structure, is largely driven by emergent behavior. For example, no rule requires that any player should fold, but usually many players do. Because the game is driven by emergent behavior, play at one poker table might be radically different from that at another, while the rules of the game are exactly the same.
Emergent structures are patterns not created by a single event or rule. There is nothing that commands the system to form a pattern, but instead the interactions of each part to its immediate surroundings causes a complex process which leads to order. Adding improperly, one might conclude that emergent structures are more than the sum of their parts.
A biological example is an ant colony. The queen does not give direct orders and does not tell the ants what to do. Instead, each ant evaluates what job it should be doing by seeing what other ants are doing, blindly follows pheromone trails, and never receives an order. Here each ant is a self-governing unit that makes choices depending only on what it 'sees'. Despite the lack of hierarchy of command, ant colonies exhibit complex behavior and have even been able to demonstrate the ability to solve geometric problems (the ants' colonies find the maximum distance from all colony entrances to dispose of bodies.)
Emergent structures also include cities and many natural phenomena including the shape of galaxies. Because they form order despite the lack of command, emergent structures may appear to defy entropic principles.
Emergent processes or behaviours can be seen in many places, from any multicellular biological organism to traffic patterns or organizational phenomena to computer simulations and cellular automata. The stock market is an example of emergence on a grand scale. As a whole it precisely regulates the relative prices of companies across the world, yet it has no leader; there is no one entity which controls the workings of the entire market. Each agent, or investor, has knowledge of only a limited number of companies within their portfolio, and must follow the regulatory rules of the market. Through the interactions of individual investors the complexity of the stock market as a whole emerges.
Emergent structures appear at many different levels of organisation. As mentioned earlier, the spatial structure of galaxies is an emergent property of the distribution of energy and matter in the universe. Similarly weather phenomena such as hurricanes are emergent properties as is life itself. Consciousness is an emergent property of a network of living cells. Emergent self-organisation appears frequently in cities where no planning or zoning entity predetermined the layout of the city.
The study of emergent behaviours is not generally considered a homogeneous field, but divided across its application or problem domains.