All quoted content below is from complexityexplained.github.io, which we encourage everyone to explore directly (as it is full of interactive Complexity illustrations and simulations):
On what Complexity Science is and what defines a Complex System:
Complexity science, also called complex systems science, studies how a large collection of components – locally interacting with each other at small scales – can spontaneously self-organize to exhibit non-trivial global structures and behaviors at larger scales, often without external intervention, central authorities or leaders. The properties of the collection may not be understood or predicted from the full knowledge of its constituents alone. Such a collection is called a complex system and it requires new mathematical frameworks and scientific methodologies for its investigation.
On the main challenge of Complexity Science:
The main challenge of complexity science is not only to see the parts and their connections but also to understand how these connections give rise to the whole.
On the differences between Simple and Complex Systems:
In simple systems, the properties of the whole can be understood or predicted from the addition or aggregation of its components. In other words, macroscopic properties of a simple system can be deduced from the microscopic properties of its parts. In complex systems, however, the properties of the whole often cannot be understood or predicted from the knowledge of its components because of a phenomenon known as “emergence.” This phenomenon involves diverse mechanisms causing the interaction between components of a system to generate novel information and exhibit non-trivial collective structures and behaviors at larger scales. This fact is usually summarized with the popular phrase the whole is more than the sum of its parts.
On self-organization in Complex Systems:
Interactions between components of a complex system may produce a global pattern or behavior. This is often described as self-organization, as there is no central or external controller. Rather, the “control” of a self-organizing system is distributed across components and integrated through their interactions.
On adaptation in Complex Systems:
Rather than just moving towards a steady state, complex systems are often active and responding to the environment -- the difference between a ball that rolls to the bottom of a hill and stops and a bird that adapts to wind currents while flying. This adaptation can happen at multiple scales: cognitive, through learning and psychological development; social, via sharing information through social ties; or even evolutionary, through genetic variation and natural selection.
Of course, this is just a taste of all there is to learn about Complexity!
Here are some other "Intro to Complexity" references you may find interesting:
If this is the beginning of your Complexity journey, we are so excited for you! Consider joining our next Complexity Weekend cohort to accelerate your learning. Roughly 1/3 of cohort Participants are new to Complexity, so you are not alone!