There are many different models for how complex systems develop, probably the most exotic (and also the most catchy name) being Chaos Theory that is primarily based in mathematics, physics, and biology. System dynamics, that studies how feedback loops work to affect a system’s development is another method often used within business and economics. And of course, we have computational methods of Agent-Based Modeling and cellular automata that present an algorithmic explanation. Systems theory also has a model for the development of complex systems, well for all systems really, it is called the process of differentiation. Wikipedia has a good explanation of systems theory’s notion of differentiation so I am going to let it explain things.
Differentiation is a term in system theory (found in sociology.) From the viewpoint of this theory, the principal feature of modern society is the increased process of system differentiation as a way of dealing with the complexity of its environment. This is accomplished through the creation of subsystems in an effort to copy within a system the difference between it and the environment. The differentiation process is a means of increasing the complexity of a system, since each subsystem can make different connections with other subsystems. It allows for more variation within the system in order to respond to variation in the environment. Increased variation facilitated by differentiation not only allows for better responses to the environment, but also allows for faster evolution (or perhaps sociocultural evolution), which is defined sociologically as a process of selection from variation; the more differentiation (and thus variation) that is available, the better the selection. - Wikipedia
Although the above quote is discussing differentiation with respect to social systems it is equally relevant for other systems, examples being cellular differentiation the process through which cells subdivide the result being that cells become more specialized in type. We can also witness this same process within the development of technologies and economies as elements are driven to become increasingly specialized in order to achieve greater efficiency, it also results in the proliferation of relations between these now interdependent components again driving complexity.