Complex Systems, despite their names, are composed by simple components. Complexity arises from the local interactions. One of the core questions for engineering and exploiting the extraordinary properties of complex systems is how to define and use simple local rules to generate higher levels of organizations. But we must answer also the questions if this “emergence” higher levels are stable or instable, temporary or permanent and so on.

Complexity emergence is a fascinating subject of study in mathematics, physics, biology, social sciences…but not only, it is also very often considered when studying future networks as complex systems of communication, processing and networking resources.

Interestingly, this paper elaborates a view of emergence of life by analyzing the mathematical properties of autocatalytic sets (collections of molecules which catalyze each other’s reactions, helping to bring each other into existence).

Simple example of autocatalysis

Autocatalytic sets have a complex structure of their own: imagine a system of multiple loops and chains, loops within loops, mutual cross-feed relationships connecting them, inhibitory connections, preferential reactions given different substrate concentrations…like an ecosystem! Paper argues that “ self-sustaining, functionally closed structures can arise at a higher level (an autocatalytic set of autocatalytic sets), i.e., true emergence“.

What makes the approach so interesting is that the mathematics does not depend on the nature of chemistry, i.e. it is substrate independent. So the building blocks in an autocatalytic set need not be molecules at all but any units that can manipulate other units. These units can be complex entities in themselves.

Also economy is essentially the process of transforming raw materials into products that themselves facilitate further transformation of raw materials and so on. So they argue that “Perhaps we can also view the economy as an (emergent) autocatalytic set, exhibiting some sort of functional closure“.

Could it be that this theory of autocatalytic sets can provide a new mathematical approach for modeling future networks ecosystems ?