Emerence and complexity describe how systems can exhibit behaviors, patterns, and outcomes that cannot be fully understood by examining individual parts in isolation. As interactions between components increase, systems often become less predictable, more adaptive, and more sensitive to relationships, context, and feedback. Complex systems may display nonlinearity, self-organization, adaptation, and unexpected emergent behaviors that arise from the interactions within the system as a whole. Understanding these dynamics is essential for systems thinking and systems engineering, particularly when working with large-scale, interconnected, or socio-technical systems.Emerence and complexity describe how systems can exhibit behaviors, patterns, and outcomes that cannot be fully understood by examining individual parts in isolation. As interactions between components increase, systems often become less predictable, more adaptive, and more sensitive to relationships, context, and feedback. Complex systems may display nonlinearity, self-organization, adaptation, and unexpected emergent behaviors that arise from the interactions within the system as a whole. Understanding these dynamics is essential for systems thinking and systems engineering, particularly when working with large-scale, interconnected, or socio-technical systems.

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Alex Arenas, Oriol Artime, Albert Díaz-Guilera, Sergio Gómez, Clara Granell

Annalen der PhysikAnnalen der Physik

Volume 538, Issue 9, September 2026, e70288

Many complex systems cannot be understood from network structure alone, nor from continuum descriptions in isolation, because their dynamics emerge from the reciprocal coupling between discrete interaction architectures and spatially extended physical fields. This perspective article surveys mathematical and computational frameworks for such network–field systems, focusing on models in which a graph is either itself the spatial substrate of a field or is embedded in a surrounding medium that mediates transport, signaling, forcing, or spatially distributed hazards. We first introduce a unified formalism for bidirectionally coupled network–field dynamics, emphasizing observation and injection operators that link node variables to continuum processes while preserving balance laws. We then examine two major modeling classes: fields evolving directly on metric graphs, where partial differential equations are posed on network geometries with vertex matching conditions; and hybrid discrete–continuous systems, where node dynamics are coupled to fields in the ambient domain, with particular attention to port-Hamiltonian formulations that provide energy-consistent interconnection principles. Within this common framework, we discuss representative modeling applications in neurobiology, including diffusion-mediated cellular communication and extracellular neural signaling, and in infrastructure systems, where network functionality depends on spatially distributed flows, loads, and hazards. Across these examples, a common picture emerges: the field is not merely an external environment, but an active dynamical layer that reshapes effective interactions, timescales, and collective behavior. By synthesizing concepts that are often developed separately across disciplines, this perspective article aims to clarify the mathematical structure, physical interpretation, and numerical challenges of coupled network–field models, and to highlight their role as a unifying language for spatially embedded complex systems.Many complex systems cannot be understood from network structure alone, nor from continuum descriptions in isolation, because their dynamics emerge from the reciprocal coupling between discrete interaction architectures and spatially extended physical fields. This perspective article surveys mathematical and computational frameworks for such network–field systems, focusing on models in which a graph is either itself the spatial substrate of a field or is embedded in a surrounding medium that mediates transport, signaling, forcing, or spatially distributed hazards. We first introduce a unified formalism for bidirectionally coupled network–field dynamics, emphasizing observation and injection operators that link node variables to continuum processes while preserving balance laws. We then examine two major modeling classes: fields evolving directly on metric graphs, where partial differential equations are posed on network geometries with vertex matching conditions; and hybrid discrete–continuous systems, where node dynamics are coupled to fields in the ambient domain, with particular attention to port-Hamiltonian formulations that provide energy-consistent interconnection principles. Within this common framework, we discuss representative modeling applications in neurobiology, including diffusion-mediated cellular communication and extracellular neural signaling, and in infrastructure systems, where network functionality depends on spatially distributed flows, loads, and hazards. Across these examples, a common picture emerges: the field is not merely an external environment, but an active dynamical layer that reshapes effective interactions, timescales, and collective behavior. By synthesizing concepts that are often developed separately across disciplines, this perspective article aims to clarify the mathematical structure, physical interpretation, and numerical challenges of coupled network–field models, and to highlight their role as a unifying language for spatially embedded complex systems.

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Cameron Brooks, Estelle Janin, Gage Siebert, Cole Mathis, Orit Peleg & Sara Imari Walker 
Scientific Reports (2026)

The Search for Extraterrestrial Intelligence (SETI) has historically been a search for aliens like us, shaped by human-centric ideas of intelligence, communication, and technology. However, humans are not the only instance of an intelligent, communicating species on Earth, and thus not the only guide to how we might think about ETI. Here, we explore how non-human communication systems could complement existing SETI strategies, usually focused on complex, potentially decodable signals, using firefly communication as an illustrative example. Fireflies communicate their presence through evolved flash patterns that are distinguishable from complex visual backgrounds. Drawing on this strategy, we present a firefly-inspired model for detecting potential technosignatures within environments dominated by ordered astronomical phenomena, such as pulsars. Using pulsar data from the Australia Telescope National Facility, we generate simulated pulse sequences that exhibit evolved dissimilarity from the surrounding pulsar population of Earth, which would constitute a signature of intelligence embodied in a relatively simple signal. This approach shifts focus from anthropocentric assumptions about intelligence toward recognizing communication through its fundamental structural properties, specifically evolutionarily optimized contrast with natural backgrounds. Our model demonstrates that alien signals need not be inherently complicated nor must we decipher their meaning to identify them; rather, signals might be distinguishable as products of engineering or evolutionary design. We discuss implications for broadening SETI methodologies and leveraging the diverse forms of intelligence found on Earth.

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Michael Levin

Philosophies 2026, 11(5), 161

I argue that the emerging sciences of synthetic morphology and diverse intelligence suggest non-physicalist models of mind and show how they can be empirically investigated. Whence the anatomical, physiological, molecular-biological, and behavioral properties of engineered new beings that have never before existed, and do not have a history of selection? Understanding, predicting, and guiding new forms of life and mind requires characterizing a structured latent space of patterns. Developmental, synthetic, and behavioral biology should take seriously, and exploit, the kinds of non-physicalist ideas that are already a staple of Platonist mathematics. I propose the following hypotheses. (1) Patterns in this space span a highly variable degree of agency, comprising a spectrum ranging from static truths studied by mathematicians to active ones studied by behavioral scientists (i.e., some patterns on the same spectrum as mathematical truths are kinds of minds). (2) The relationship between mind and body is the same as the relationship between causally instructive mathematical facts and physics. (3) Living beings have no monopoly on the “free lunches” provided by the ingression of these patterns into the physical world. While traditional computationalist views of living and cognitive systems are insufficient, my framework erases artificial distinctions between organisms and machines, framing all physical constructs (natural or engineered) as being, to various degrees, in-formed by patterns from the latent space. I sketch a research program, already begun, inspired by these ideas. Such frameworks, while contradicting long-held assumptions of both mechanists and organicists, could have many implications for evolutionary biology, regenerative medicine, AI, and the ethics of synthbiosis with the forthcoming immense diversity of morally important beings.

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