We can calcute Shannon entropy for larger window sizes (not just the 3-cell rule neighbourhood)to quantify hierarchical self-organisation. (here window size is 5)
'Self-organization is a dynamical process by which a system spontaneously forms nontrivial macroscopic structures and/or behaviors over time.' H. Sayama 2015 p. 6 via Lizier 'Information Theory for analysing Complex Systems' Module 6