Complexity, Complex Adaptive System (CAS), Cellular Automata (CA)
Adapted from the article originally written by Abena Sekyere
for the Cabrera's Cornell University, System Thinking in Public Affairs Course
Complexity science is the study of complex systems and their multidimensional, unpredictable, and difficult problems. Furthermore, complexity science is not limited to one specific theory like chaos theory or systems biology but rather, it encompasses various theories and tools across multiple disciplines and explores the diverse relationships between them  &.
A core aspect in the study of complexity science is Complex Adaptive Systems(CAS). CAS are systems consisting of multiple agents interacting in nonlinear ways that are able to adapt to become better suited to their environment.  In CAS ,interacting agents are able to self-organize from ‘simple’, fundamental principles which results in the emergence of surprising or complex behavior. Example: immune systems, developing embryos and ecology.
Figure 1: CAS 
Among the trailblazers of complexity science and CAS is the
Santa Fe Institute, a complexity science research facility, founded by great minds like Murray Gell-Mann to advance its study and application in numerous fields like economics, artificial intelligence, and biology.
The following are the core principles in complexity science:
Nonlinearity: No direct cause and effect since there are
numerous factors and relationships occurring
Diversity: It can be analyzed and applied across various
Emergence: Complex behavior can come out of from
simple, local rules 
Self-Organization: Agents continuously organize
themselves in the absence of a leader
Complexity science most likely belongs to the fourth wave because CAS is fundamental to the current wave of how systems think and how we think of them.
An illustrative example of CAS is a flock of birds that travel in an orderly fashion in the absence of a leader. The outcome of equidistance and order emerges from simple rules in nature through which they self-organize and fly in such an incredibly orderly pattern.  Healthy Immune systems are another example of CAS. The immune system consists of antibodies that repel or destroy antigens. Since these invaders come in numerous forms, the immune system cannot realistically list all possibilities of antigens it would have to fight. Instead, it is able to adapt its antibodies as new invaders come.
Complex Adaptive systems are fundamental to important systems such as Agent-Based Modelling(ABM) and Cellular Automata(CA). ABM is a kind of CAS is modeled as a collection of autonomous decision-making entities called agents which make individual assessments of situations and decisions based on a set of rules. In ABM, emergent behavior is nonlinear and self- organized. Cellular automata is a collection of cells on a grid which with time, are able to evolve based on some rules governed by the state of their neighboring cells. An example of this is Rule 90 in the chessboard where the squares of the same color cannot be immediately next to each other both vertically and horizontally.
ABM and CA are similar because as CAS’ they both employ self- organization and the agents/cells interact based on a set of rules. On the other hand, they are very different because CA is generally simpler than ABM. While CA at very complex levels deals with presenting universality with a more complex average of adjacent cells, ABM involves application where more complex emergent phenomena arise such as traffic flows and stock markets. Understanding CA and ABM is necessary because it reveals the importance of self organization and how CAS’ can have varying levels of complexity and diverse forms of application in numerous disciplines.
An example of how complexity science(CAS) is used to solve problems is in a project by the Santa Fe Institute to gain a better understanding about why some human societies are more unequal than others. In the last ten years, the research has brought together anthropologists, economists and historians to analyze the interconnection between people and the societal structures and how the emergent structure of inequality exists as a whole. 
- CAS is an important fundamental principle to complex systems thinking
It is interdisciplinary and not limited to one theory
Might be a little difficult to simulate these systems because of how adaptive they are in real life; challenging to model all possibilities
References and Further Reading
- Benham-Hutchins, M. and Clancy, T. (2010). Social Networks as Embedded Complex Adaptive Systems. JONA: The Journal of Nursing Administration, 40(9), pp.352-356.
- Lansing, J. (2003). Complex Adaptive Systems. Annual Review of Anthropology, 32(1), pp.183-204.
- Paley, J. and Eva, G. (2011). Complexity theory as an approach to explanation in healthcare: A critical discussion. International Journal of Nursing Studies, 48(2), pp.269-279.
- Cabrera, D. and Cabrera, L. (2015). Systems thinking made simple. 2nd ed. Pletica.
- Holland, J. (1992). Studying Complex Adaptive Systems. A New Era in Computation, 121(1), pp.17-30.
- Inamdar, A. (2018). Importance of making organisations adaptive | UpRaise. [online] UpRaise. Available at: https://upraise.io/blog/making-organisations- adaptive/
- Thurner, S., Hanel, R. and Klimek, P. (2018). Introduction to the theory of complex systems. Oxford University Press.
- Atkisson, Curtis; Piotr J. Gorski; Matthew O. Jackson; Janusz A. Holyst and Raissa M. D’Souza. (2019) Why understanding multiplex social network structuring processes will help us better understand the evolution of human behavior.
- Iyengar, G., Kets, W., Sethi, R. and Bowles, S. (2008). Inequality and Network Structure. SSRN Electronic Journal.
- Bonabeau, E. (2002). Agent-based modeling: Methods and techniques for simulating human systems. Proceedings of the National Academy of Sciences, 99(Supplement 3), pp.7280-7287.
- Weisstein, E. (2019). Cellular Automaton -- from Wolfram MathWorld.[online] Mathworld.wolfram.com. Available at: http://mathworld.wolfram.com/CellularAutomaton.html [Accessed 23 Sep. 2019].