The architecture of complexity

We are surrounded by complex systems, from cells made of thousands of molecules to society, a collection of billions of interacting individuals. These systems display signatures of order and self-organization. Understanding and quantifying this complexity is a grand challenge for science. Kinetic theory, developed at the end of the 19th century, shows that the measurable properties of gases, from pressure to temperature, can be reduced to the random motion of atoms and molecules. In the 1960s and 1970s, researchers developed systematic approaches to quantifying the transition from disorder to order in material systems such as magnets and liquids. Chaos theory dominated the quest to understand complex behavior in the 1980s with the message that unpredictable behavior can emerge from the nonlinear interactions of a few components. The 1990s was the decade of fractals, quantifying the geometry of patterns emerging in self-organized systems, from leaves to snowflakes.