Topological constraints on self-organization in locally interacting systems
Francesco Sacco, Dalton Sakthivadivel, Michael Levin; Topological constraints on self-organization in locally interacting systems. Philos Trans A Math Phys Eng Sci 14 May 2026; 384 (2320): 20250011. https://doi.org/10.1098/rsta.2025.0011 Download citation file: All intelligence is collective intelligence, in the sense that it is made of parts that must align with respect to system-level goals. Understanding the dynamics that facilitate or limit navigation of problem spaces by aligned parts thus impacts many fields ranging across life sciences and engineering. To that end, consider a system on the vertices of a planar graph, with pairwise interactions prescribed by the edges of the graph. Such systems can sometimes exhibit long-range order, distinguishing one phase of macroscopic behaviour from another. In networks of interacting systems, we may view spontaneous ordering as a form of self-organization, modelling neural and basal forms of cognition. Here, we discuss necessary conditions
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