Systems are composed of well- defined components that, when integrated, act together to form a functioning entity. Identifying a system or a hierarchy of systems requires a certain level of abstraction and simplification. Simple systems have few components, and their behaviour is fully understandable and predictable. Consider a ball falling through the air; this simple system consists of the ball falling under the influence of the gravitational force with a viscous drag. Add more balls and this system becomes complex: vortices from each ball affect the fall of the other balls in a manner that cannot be simply extrapolated from the fall of a single ball.
Complex systems have many components that interact to create a functioning unit without an overarching regulatory body1. It is the self-organized cooperative interaction of the individual components that determines the emergent functionalities.
Complex self-organizing systems are prevalent in nature. They are part of our everyday lives in areas ranging from ecology, sociology and economics, to biology, medicine, chemistry and physics. Many systems share similar spatio-temporal structures. For example, one might ask whether the large-scale periodic structure of sand dunes is related to the nanoscale patterns of polymer microstructures, whether the turbulence is similar in stars and in a stirred coffee cup or whether cardiac fibrillation is related to the aggregation dynamics of social amoebae. It is remarkable that these statements are true.
Numerical simulation and advanced experimental tools now allow detailed quantitative investigations of the spatio-temporal evolution of complex systems, including not only spatially extended systems2, but also highly coupled networks. This is well illustrated by the example of epidemic outbreaks and the subsequent geographic spreading of infectious disease, which incidentally mirrors the transportation of banknotes.