The epochal paper of 1972 by Phil Anderson “More is Different” has set the paradigm for what has now evolved into the science of complexity. The idea that “reality has a hierarchical structure in which at each stage entirely new laws, concepts, and generalizations are necessary, requiring inspiration and creativity to just as great a degree as in the previous one” has set a new perspective in our view of many natural phenomena.
The reductionist view focuses on the elementary bricks of which matter is made, but then these bricks are put together in marvelous structures with highly elaborated architectures. Complexity is the study of those architectures, which depend only partially on the nature of the bricks, but also have their fundamental laws and properties, which cannot be deduced from the knowledge of the elementary bricks.
In the study of dynamical processes which can give rise to complex geometrical structures, it was noticed that often these are strongly out of equilibrium and dissipative processes, where elementary constituents have non trivial mutual interactions, with an evolution which is characterized by a certain degree of self-organization leading to the formation of collective properties.