Emergence: Complexity From Simplicity

Today’s guest post is by Jochen Fromm, a scientist and software engineer from Berlin, who is the founder of the Complex Adaptive Systems, CAS, group blog. He holds a degree in theoretical physics and has interests in complex systems, emergence, self-organization and, especially, multi-agent systems.

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As John H. Holland explains in the video that follows, emergence is one of the central principles that explain how complexity can arise from simplicity or how order comes out of chaos. It happens when large-scale order arises from small-scale interactions. In complex systems, simple rules can have complex results and small events can have great effects.

Classic examples are flocks of birds and shoals of fish. How they move as one is mysterious and fascinating. The first steps towards understanding this behavior was made by Craig Reynolds in 1986, who programmed the basic rules of bird motion into a computer. His agent-based model "Boids" shows how complex swarms can arise from simple interactions between agents following rules.

The Rules for swarms or flock of birds are simple: stay away from your neighbors, but stay close to the group. A swarm is a group of followers without leader. Global attraction (a move towards the group) is combined with local repulsion (stay away from individuals). Reynolds formulated three basic rules:

·            Separation: steer to avoid crowding local flockmates

·            Alignment: steer towards the average heading of local flockmates

·            Cohesion: steer to move toward the average position of local flockmates

Agent-based models like the boids model are key to understanding the principles of emergence and swarm intelligence (the collective intelligence of swarms). These principles in turn explain how simple rules can have complex results. 

Yet there is also a downside: although simple rules can lead to complex results, in most cases they do not. And not every group moving in synchronized ways is good.

Emergence happens with all kinds of living things that live in groups. An army marching in formation is fascinating, too, but these forms of "forced swarms" are certainly more controversial. Einstein said "that a man can take pleasure in marching in formation to the strains of a band is enough to make me despise him," but people find marching armies fascinating for the same reason they like swarms. We admire the fascinating unity in diversity in moving crowds, flocks of birds or shoals of fish.

The essence of many agent-based models is a conflict. In the boids model, the problem is that the neighbors don’t have the right place or position. Each agent wants to be close to the group, but also wants to stay away from the other individuals. Many small conflicts about the right position in the neighborhood lead to large clusters of similar positions in the form of swarms.

Similar effects occur in models for human society, for example Thomas Schelling’s Segregation Model for ghetto formation and Robert Axelrod’s Dissemination Model for culture formation. In the first model, neighbors are of different races, while, in the latter, neighbors don’t have the same traits. Schelling showed that a small preference for one’s neighbors to be of the same race could lead to total segregation. Axelrod showed that a small preference for one’s neighbors’ traits could also lead to segregated cultures.

There are many other fascinating agent-based models and more complicated forms of emergence. What they all have in common is that the behavior emerges from actions controlled by the rules of the model. The behavior of the whole is more than the sum of the parts.

Emergence and swarm intelligence are not the only principles at work in these systems, however. Path dependence, lever points, frozen accidents and butterfly effects, all subjects for future posts, also help explain how small events can have great effects in complex adaptive systems.