IV. Ecosmomics: Independent Complex Network Systems, Computational Programs, Genetic Ecode Scripts

Amaral, L. and J. Ottino. Augmenting the Framework for the Study of Complex Systems. European Physics Journal B. 38/2, 2004. An introduction to a special issue on the ubiquitous presence of scale-free dynamic networks from food webs and epidemics to neural phenomena and especially the worldwide Internet. In this regard a generic definition of complex systems is attempted, see the quote below. These elemental units and interactions then self-organize into a universal, nested self-similarity.

A complex system is a system with a large number of elements, building blocks or agents, capable of interacting with each other and with their environment. The common characteristic of all complex systems is that they display organization without any external organizing being applied. The whole is much more than the sum of its parts. (148)

Andersen, Benjamin, et al. Evidence of universal conformal invariance in living biological matter. Nature Reviews Physics.. March, 2025. Eight computational physicists posted at the University of Copenhagen, University of Lisbon, University of Lausanne and University of Sheffield press on with mid 2020s complexity studies so to provide another theoretical perspective upon nature’s universal, recurrent lawfulness. A notable difference is that they begin with physical inorganic materials which are seen to likewise express organized structures known as conformal invariance. The project continues to biological phases where the view prompts a further way to perceive a constant viable criticality. Our planatural philoSophia take is to then suggest that these many current integral insights we record seem just now coming to their phenomenal realization and factual discovery.

The emergent dynamics of collective cellular movement depend on how cells interact and move across biological systems. Here we report experimental evidence of a universal feature in the patterns of flow that spontaneously emerge in cellular groups. Specifically, we show that the flows generated by dog kidney cells, human breast cancer cells and pathogenic bacteria exhibit robust conformal invariance. This constant recurrence reveals that the macroscopic features of living biological matter exemplify universal translational, rotational and scale symmetries that are independent of their microscopic constituents. (Abstract)

Although many attempts have been made to model the patterns of collective movement made by organisms, we still lack a general unifying theory. In contrast, the study of complex interactions between the components that make up inanimate materials has led to common behaviours near critical regimes. The principles that give rise to this universality have been described using the framework of conformal field theory, which predicts how shapes and angles of structures are locally conserved across different systems. (1)

In this paper, we experimentally demonstrate that the patterns of collective movement observed in different types of living matter exhibit common characteristics that transcend the properties of the cells from which they are composed. We show that many instances including colonies of pathogenic bacteria, groups of collective kidney cells and breast cancer cells, spontaneously generate flows that exhibit a universal conformal invariance described by the percolation universality class. (2)

These results suggest that the theories used to describe conformally invariant structures might have a much broader range of applications. Although our results do not necessarily indicate that the collective movement we observe is operating at the critical point of a phase transition, many different biological systems are thought to be poised near criticality which allows them to easily switch between different states. Our findings, thus, imply that the mathematics to study conformally invariant structures could also lead to new methods to detect and understand critical phenomena in biology. (5)

Anderson, Philip. More Is Different - One More Time. N. Phuan Ong and Ravin Bhatt, eds. More Is Different. Princeton: Princeton University Press, 2001. The Nobel laureate physicist revisits his landmark 1967 paper which helped turn science from a fixation on subatomic domains to the complexity revolution.

The actual universe is the consequence of layer upon layer of emergence, and the concepts and laws necessary to understand it are as complicated, subtle and, in some cases, as universal as anything the particle folks are likely to come up with. (7)

Anderson, Philip, et al, eds. Downward Causation. Arrhus, Denmark: Arrhus University Press, 2000. Papers that explore how self-organizing, agent-based systems lead to an increasing influence by ‘higher,’ more consciously informed levels, over lower or prior stages, which is present from physical theory to literary genres.

Araujo, Nuno, et al.. Steering Self-Organization through Confinement. arXiv:2204.10059. This entry is a composite synopsis of a June 2021, Leiden University Lorentz Center workshop on the title topic, which can serve as an overview of the 21st century scientific revolution to date. Some 29 attendees from Europe and the USA included Liesbeth Janssen, Simon Garnier, and Audrey Dussutour. A novel agenda went on to consider how certain system boundaries can have a formative effect on this dynamic development process. As the quotes allude, from our late vantage, the broad field of complexity studies over 50 years (which this site seeks to report) can be seen as a singular, WorldWise revolutionary endeavor which is just coming a convergent, self-similar synthesis from uniVerse to wumanVerse.

In regard, at this consummate moment, the outlines of a general scenario that is much akin to life’s developmental genotype and phenotype basis can become quite evident. Physical models, for example, cite implicate/explicate and informative bit/it versions. Altogether the whole ecosmic genesis appears to be suffused by an independent, universally present, mathematic code-script which serves to engender and self-organize at each and every scale and beingness. As a consequence, astro biochemicals, evolutionary organisms, entities in groups, communicative mores, societal processes and all else arise, complexity, and quicken in an oriented fashion wherever they can. As life’s emergence thus goes forth, these myriad phenotypes come to exemplify the familial source in their complementary bigender, whole occasion. So into this fraught 2022 year, an epochal, once and future true universality can at last be affirmed.

Self-organisation is the spontaneous emergence of spatio-temporal structures and patterns from the interaction of smaller individual units. Examples are found across many scales from physics, materials science and robotics to biology, geophysics and astronomy. Recent research has found that self-organisation is mediated and controlled by local boundaries which then steer the emergence or suppression of collective phenomena. Here we consider a common framework for future research and scientific challenges across disciplines. We hope this endeavor will advance deeper appreciations of natural self-organisation for novel material, biological and societal benefits. (Abstract excerpt)

From molecular aggregates to groups of animals and human crowds, from microswimmers to granular materials and robotic swarms, systems that self-organise can be found across a wide diversity of length and time scales. The dynamic concept arose in the later 20th century and defines the spontaneous emergence of large-scale collective structures and patterns from the interaction of many individual units, such as molecules, colloidal particles, cells, animals, robots, pedestrians or even astronomical objects. These units can be heterogeneous in size, shape, composition and function. (3-4)

We can thus define confinement in self-organisation as anything which causes units to localise to a region of space at a given time. The variety of self-organising systems influenced by confinement spans s wide range of length scales from active filaments driven by microscopic molecular motors enclosed within living cells, to the emergence of macroscopic coherent flow structures confined by Earth’s atmosphere, to the formation of entire galaxies under the pull of the gravitational potentials of black holes. While confinement is not always required for a system to self-organise [17], it can play a pivotal role as either a catalyst or inhibitor for self-organisation. (5)

In conclusion, steering self-organisation through confinement is a very active and rapidly evolving field of research, which is intrinsically multidisciplinary. To push the field forward, the scientific community working on self-organisation should increasingly take advantage of the cross-fertilisation of ideas that results from sharing hypotheses, theoretical approaches and experimental methods among experts from different fields and disciplines. This perspective article provides a first step in this direction. (11)

Artime, Oriol and Manilo De Domenico. From the Origin of Life to Pandemics: Emergent Phenomena in Complex Systems.. Royal Society Proceedings A. May, 2022. After an historic and topical survey, as the Abstract notes, the University of Padua biophilosophers consider spontaneous appearances from quantum/classical physical realms to life’s evolutionary development and onto social occasions. In each case mathematical principles, criticality phases and complex, dynamic network are seen to have a central role. Some entries are Emergence and Algorithmic Information by P. Abrahao and H. Zenil, Emergence of Functional Information from Multivariate Correlations by C. Adami and C. Nitash, and Emergent Entanglement and Self-Similarity in Quantum Spin Chains by B. Sokolov, et al. Into the 2020s, a strongly evidential presence of consistent universality can be glimpsed from universe to us peoples.

When a large number of similar entities interact among each other and with their environment at a lower phase, unexpected outcomes at higher spatio-temporal scales might spontaneously arise. This nontrivial phenomenon, known as emergence, characterizes a broad range of distinct complex systems -- from physical to biological and social ones -- and is often related to collective behavior. It is ubiquitous from oscillators that synchronize to animate birds flocking or fish schooling. Despite the ample phenomenological evidence of their existence, theoretical questions about emergence remain still unanswered. We offer a general overview and sketch current and future challenges. Our review also introduces this Theme Issue "Emergent phenomena in complex physical and socio-technical systems: from cells to societies", which covers the state of our understandings from life’s origins to the expansive propagation of infectious diseases. (Abstract excerpt)

Aschwanden, Markus, et al. Order Out of Randomness: Self-Organization Processes in Astrophysics. arXiv:1708.03394. Reviewed at length in Systems Cosmology, this is an 18 author, 97 page treatise which could be seen as a premier affirmation of an inherently nonlinear, lively, complexifying cosmic genesis.

Ashtiani, Minoo, et al. A System Survey of Centrality Measures for Protein-Protein Interaction Networks. BMC Systems Biology. 12/80, 2018. Our interest in this entry by bioinformatic theorists with postings in Iran and Germany is to record in 2018 how this biochemical domain can be treated by the same multiplex geometries as neural brains. In reflective regard, we peoples may at last be able to confirm the natural presence from quantum and genomic to cerebral and cosmic realms of a node/link, DNA/AND, universe to human image.

Numerous centrality measures have been introduced to identify “central” nodes in large networks. The availability of a wide range of measures for ranking influential nodes leaves the user to decide which measure may best suit the analysis of a given network. The choice of a suitable measure is furthermore complicated by the impact of the network topology on ranking influential nodes by centrality measures. To approach this problem systematically, we examined the centrality profile of nodes of yeast protein-protein interaction networks (PPINs) in order to detect which centrality measure is succeeding in predicting influential proteins. We studied how different topological network features are reflected in a large set of commonly used centrality measures. (Abstract)

Auffray, Charles, et al. Self-organized Living Systems. Philosophical Transactions of the Royal Society of London A. 361/1125, 2003. After centuries of the reductionist method which identified the components of nature, a new biosystemic paradigm is recommended which can integrate the relational dynamics of living entities and processes. In this view, biology is a science of information in a hierarchical flux, formed by a creative balance between order and chaos.

Azpeitia, Eugenio, et al. Cauliflower Fractal Forms Arise from Perturbations of Floral Gene Networks. Science. 373/192, 2021. A cover image entry by a 14 member biomathematician team with postings in France, Italy, UK, USA, and Spain which further quantifies nature’s innate iterations in kind which serve to form and express such vital geometries. Their novel contribution is to associate their artistry with a genetic source. One is moved again to ask however (whomever) did all this mathematic scriptome get there in the first place. See also Cauliflower and Chaos, Fractals in Every Floret by Sabrina Imbler in the New York Times for July 9, 2021.

Throughout development, plant meristems regularly produce organs in defined spiral, opposite, or whorl patterns. Cauliflowers present an unusual organ arrangement with a multitude of spirals nested over a wide range of scales. How such a fractal, self-similar organization emerges from developmental mechanisms has remained elusive. Combining experimental analyses in an Arabidopsis thaliana cauliflower-like mutant with modeling, we found that curd self-similarity arises because the meristems fail to form flowers but keep the “memory” of their transient passage in a floral state. This study reveals how fractal-like forms may emerge from the combination of key, defined perturbations of floral developmental programs and growth dynamics. (Abstract)

Bak, Per. How Nature Works. New York: Springer, 1996. The late Danish systems scientist provides a succinct account of self-organized criticality poised between order and chaos, a theory which he originated.

Balaban, Valeriu, et al. Quantifying Emergence and Self-Organization of Enterobacter cloacae Microbial Communities. Nature Scientific Reports. 8/12416, 2018. Amongst a flurry of 2018 papers, University of Southern California bioengineers including Paul Bogdan (search) show how nature’s universal complexities are iconically manifest in this prokaryote phase. Once again, a generic process is observed as active, informed agents emerge into complex, modular, nested networks with a collective intelligence. See also Multi-fractal Characterization of Bacterial Swimming Dynamics by this group (Hana Koorehdavoudi, et al) in Proceedings of the Royal Society A (473/2017.0154).

From microbial communities to cancer cells, many such complex collectives embody emergent and self-organising behaviour. Such behaviour drives cells to develop composite features such as formation of aggregates or expression of specific genes as a result of cell-cell interactions within a cell population. Currently, we lack universal mathematical tools for analysing the collective behaviour of biological swarms. To address this, we propose a framework to measure the degree of emergence and self-organisation from scarce spatial data and apply it to investigate the evolution of Enterobacter cloacae aggregates. Multifractal analysis was used to characterise these patterns and calculate dynamics changes in emergence and self-organisation within the bacterial population. (Abstract excerpt)

The multifractal spectrum is the central part of any multifractal analysis and can be used to describe the group properties of interacting agents, such as bacteria aggregates. The multifractal analysis investigates the statistical scaling laws of complex fragmented geometrical objects which cannot be described by classic geometric methods. Considering that microbial communities exhibit complex time-varying aggregation patterns, we employ
the above-mentioned multifractal formalism to characterise the phase-space dimensionality and complexity of the observed dynamics. Consequently, interpreting the microbial community as an intelligent system driven by heterogeneous interactions meant to cooperate for achieving a collective goal allows us to develop two approaches for quantifying the instantaneous degree of emergence and self-organisation in collective system. (5)

Self-organisation, similar to emergence, denotes a collective behaviour and represents the ability of a group to drive the system towards an ordered state. During this transition, all group members, independently and in the absence of a centralised controller, adjust their actions to increase the order of the whole. (6) Collective behaviour refers to complex macroscopic dynamics of microbial communities exhibiting emergence and self-organisation properties without a global controller. Alternatively stated, the cognitive abilities and the adaptation to environmental changes are distributed among individuals forming the group. The emergent behaviour in systems ranging from microbial communities to carcinogenic systems and somatic cellular societies generates complex qualities not present at the individual level such as information generation, collective memory, and efficient cell-to-cell communication. (6)

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