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The Complexity Explorer site provides online courses and other educational materials related to complex systems science. The Complexity Explorer project is being developed by the Santa Fe Institute and is funded by a grant from the John Templeton Foundation and by user donations.

Time in complex systems operates concurrently at different scales, runs at multiple rates, and integrates the function of numerous connected systems. We describe these processes as "complex time" as opposed to the simple, regular clock time of physical phenomena. In complex time age includes explicitly the coupling between information gain and information loss.

The rise of the state is a key marker in the evolution of human society. States typically emerged when one chiefdom (amid a competing set of chiefdoms) achieved a greater and more effective level of organization.
Despite the presence of similar conditions, some states rose and flourished while some advanced chiefdoms never passed the threshold into statehood. Why states emerged in some places and not others, why they arose independently in six places around the world starting about 5,000 years ago, and why their rise was usually associated with the growth of cities, are fascinating questions for anthropologists. Answers to these questions could offer insights into today's urban systems.

The Santa Fe Institute is a nonprofit, independent research center that leads global research in complexity science. SFI scientists seek the shared patterns and regularities across physical, biological, social, and technological systems that give rise to complexity-in any system in which its collective, system-wide behaviors cannot be understood merely by studying its parts or individuals in isolation. Insights from complexity science are increasingly useful in understanding questions far beyond the boundaries of traditional academic disciplines-urban sustainability, disease networks, and financial risk, to name a few.

SFI's Cities, Scaling, and Sustainability research effort is creating an interdisciplinary approach and quantitative synthesis of organizational and dynamical aspects of human social organizations, with an emphasis on cities. Different disciplinary perspectives are being integrated in terms of the search for similar dependences of urban indicators on population size - scaling analysis - and other variables that characterize the system as a whole. A particularly important focus of this research area is to develop theoretical insights about cities that can inform quantitative analyses of their long-term sustainability in terms of the interplay between innovation, resource appropriation, and consumption and the make up of their social and economic activity. This focus area brings together urban planners, economists, sociologists, social psychologists, anthropologists, and complex system theorists with the aim of generating an integrated and quantitative understanding of cities. Outstanding areas of research include the identification of general scaling patterns in urban infrastructure and dynamics around the world, the quantification of resource distribution networks in cities and their interplay with the city's socioeconomic fabric, issues of temporal acceleration and spatial density, and the long-term dynamics of urban systems.

About the Course: We have re-opened our popular introductory course indefinitely; all units will be open once the course is launched. You will be able to complete this course at any time of the year and receive a certificate. There will be a course instructor offering office hours and monitoring the forums to support your complexity learning journey. 

"Fractals are scale-free, in the sense that there is not a typical length or time scale that captures their features.  A tree, for example, is made up of branches, off of which are smaller branches, off of which are smaller branches, and so on.  Fractals thus look similar, regardless of the scale at which they are viewed.  Fractals are often characterized by their dimension.  You will learn what it means to say that an object is 1.6 dimensional and how to calculate the dimension for different types of fractals."