These results suggest the possibility that criticality could be diagnosed and induced directly from the maintenance of a given distribution of correlations rather than modelling a precise mechanistic structure. Also, our results show that criticality could be generated by quite simple mechanisms only relying on local information, maintaining specific correlations around a given value. Here we have implemented the mechanism as a simple Boltzmann Learning process, but other rules could have the same effect, such as the combination of Hebbian and anti-Hebbian tendencies in specific ratios or other simple mechanisms. In our model, we only require the system to maintain a distribution of relations between the components of the system. This connects with systemic approaches to biology interested not in specific or intrinsic components of biological systems but in the networks of relations and processes26–28. It is also in line with notions of relational invariance in Piaget’s approach to functional invariants in cognitive development29 or Maturana and Varela’s ideas of autopoietic machines, defined as homeostatic systems that maintain their own organization constant as a network of relations between components30.