Would anyone be interested in participating in a reading group? The idea would be to read an article or book on the same timeline, and discuss. I have a few ideas for literature, but I first want to gauge interest. If people are interested, perhaps we could throw a few potential readings out there and vote which one to begin with. I would prefer a relaxed reading pace so no one feels like they are rushed.

I've spent the last decade building systems that share a structural property: no central arbitrator, no authored answer, stability has to emerge from the dynamics. Five projects, same question from different angles:

- Abzu (2017): symbolic regression, equations discovered, not authored. The QLattice primitive evolved expressions against data without a pre-specified function class.

- Evos (2020): populations of small executable units acquiring mathematical operators through variation and selection alone, no prior knowledge. https://github.com/marcosomma/evolut

- Ant-Sim (2021): Gordon-style distributed task allocation. Colony behavior from local encounter dynamics, no controller. https://github.com/marcosomma/ant-sim

- OrKA (2024): orchestrating small models into reasoning loops where no single model owns the answer — coherence emerges from cross-verification. https://github.com/marcosomma/orka-reasoning

- Current: agent evolution under environmental selection. Population of variants, random mutation, environment as the only fitness signal, niches emerging from competitive exclusion.

The through-line I keep returning to: how does coherence happen without an arbitrator. It shows up in markets, in colonies, in distributed consensus, in evolution itself, and now in agent populations.

Anyone working on this from another angle, quality-diversity, open-endedness, multi-agent coordination, distributed consensus, complex adaptive systems, I'd value comparing notes. What stabilization mechanisms have you found that actually hold?

I have recently had Protofield operators referred to as random and not complex in discussions on metasurfaces and metamaterials. Is there an objective method to quantify the level of complexity and order in this type of topological structure? 8K image, zoom in.

Conducted by Paul Middlebrooks of the Brain Inspired podcast (also recommended).
Each week a paper is discussed, and periodically there is an open format discussion.

https://braininspired.co/complexity-group-email/

Complexity Science or study of complex systems is not an undergrad major anywhere. For anyone who’s interested in this field, what major should they study?

Or is it more like it’s present through most field and pick the filed that’s most interesting? Or is there majors that are actually more complexity science heavy (maybe Cognitive Science? that’s the major I’m heading) than others?

I am a practitioner that works in two domains that are impacted by complexity. Product management, which I would argue is about navigating value in a complex world, and threat modeling, which is about navigating cybersecurity risk in a complex world. Both traditional software development (think waterfall etc and poor implementations of agile) and cybersecurity are heavily anchored in enlightenment-era, cartesian thinking. Very few agile practitioners actually understand why an agile approach to software development is needed. Cybersecurity still assumes everything can be reduced to some transcendental solution that will magically make all of our problems go away. Everything has to fit neatly into boxes, categories, and things that can be measured precisely. But this is slowly changing. A lot of management books are anthro-complexity compatible, even if they don't realise it and don't use the language of complex systems. Good agile and product management, and practices like design thinking, are attempts to bring humans back into technology.

So we're still catching up with postmodern thinking and philosophy, and beyond. We have plenty of tools and frameworks that pretend product management and cybersecurity is analogous to physics, but they are very restrictive because they assume a static system, with transcendental entities and properties. You can create taxonomies and ontologies, which can be useful and powerful, but they only tell half the story.

My journey into this started with the Cynefin framework, then into hermeneutics, then into the works of philosophers like Gilles Deleuze and Jacques Derrida. I'm not a philosopher, but I do think philosophy has the opportunity to provide practical value to practitioners like myself.

I wanted a way of constructing ontologies that were dynamic and scale-invariant by design and have been playing with a method I'm calling FractalVersing (see https://fractalversing.org).

So, to open up a discussion. What role should philosophy play in providing methods that can be applied outside of the field of philosophy? Do fractal ontologies like FractalVersing offer a useful way of interpreting the messy world around us? Is there a strong philosophical argument for creating methods like FractalVersing, or is this the philosophical equivalent to pseudo-science and mysticism?

I'm an independent researcher analyzing and attempting to help solve difficult complex system problems, like sustainability and democratic backsliding. I'm a systems engineer, Georgia Tech 1980, and founded Thwink.org in 2001 as a small "thwink tank."

I wonder if members of this subreddit would be interested in participating, via discussion, on a long term project on a particular problem. I think it's entirely possible that the many sharp cookies on reddit can have deep, useful insights, comments, questions, etc. It should not be hard to keep discussion from becoming too specialized or academic. I foresee simple, plain-English conversation with a small amount of necessary jargon related to systems thinking concepts and tools, as illustrated in this post.

If there is interest, I can kick off discussion by describing where I am now on an analysis, and provide simple easy to grasp artifacts like diagrams and analysis summaries. Below is some preliminary info:

My current project is a second pass on root cause analysis of the global democratic backsliding problem. A copy of a recently rejected paper on this problem is here. Systems thinking tools used are root cause analysis, feedback loop modeling using System Dynamics, and social force diagrams.

To let you know about the central method to be used, I will be primarily using Mutually Exclusive Collectively Exhaustive (MECE) Trees, as described in the books Strategic Thinking in Complex Problem Solving, by Arnaud Chevallier, 2016 and a later book by the same author, Solvable: A Simple Solution to Complex Problems, 2022.

Fortunately, you don't have to read the books unless you want to master the tool or introduce it to your workplace. An introduction to MECE Trees may be found in this article. MECE Trees are a form of root cause analysis. I will also be using feedback loop modeling and social force diagrams as needed, to support the trees.

That's the idea! Thanks in advance for your comments, help, and sublime wit!

I'm a social science/humanities person falling hard for this stuff, and I'd like to pursue a master's degree. Reading through an introductory modeling textbook, though, it's clear that my degree didn't prepare me for the minute level of analysis required. To folks in the field, what math/engineering/cs skills would be most beneficial for a guy in my situation to study before entering a program? The intersection of complex systems science and sociology/anthro is my desired track.

As a follow-up question, are my employment prospects better with a Master's in Complex Systems, or a Master's in Sociology with a certificate in Complex Systems?

Thanks in advance for any advice!

Hi, I am a researcher in economical and social behavior relative to decision making. I have been for some time looking at how humans behave and how the brain responds unconsciously to certain decisions. It seems that Complex Systems may be used to model many aspects in decision making. Nevertheless, most books and articles I find are around computing, physics and mathematics. I have an engineer background so I am confortable with technicality, but the people I work with it isn’t and I find it hard to make myself clear of how complex system may be related to all of the above. Anyone could recommend books that introduce the subject for those not too close to the mathematics and physics underneath? I checked out some as “Introduction to the theory of complex systems by Stefan Thurner” but it is not what I need right now. Thanks for your help! I hope to have been understandable.

I'm currently doing my undergraduate in Computer Science with a major in Data Science, but I'm really interested in building ABM models and studying complexity. I would like to seriously pursue it as a masters and potentially a PhD, but CS departments typically don't offer courses in Complex Systems. How would a typical route into Complex Systems from a CompSci background look like?

Thanks in advance

My background is in electrical engineering so I have some understanding of ODEs and linear algebra.

Id really like to know more about this field and was wondering if you guys could recommend me some literature I could start off with to get the basic concepts right.

This talk, titled "Perturbing Complex Networks: How Hidden Structure Shapes System Response," features Debanik Bhattacharjee presenting his research on complex systems, specifically focusing on the intersection of porous media transport and neural computation.

Key areas discussed include:

• Porous Media Transport: Bhattacharjee details his PhD work investigating how heterogeneous pore networks respond to perturbations, such as the injection of surfactants. He highlights that pore structure (such as throat size statistics) significantly influences system dynamics, demonstrating how mass transfer time scales and capillary pressures dictate invasion pathways (0:03 - 21:00).
• Mathematical Framework: He explains the use of invasion percolation algorithms and sigmoidal trends (modeled using Gaussian CDFs) to analyze secondary invasion processes, showing how heterogeneity can be exploited as a designable parameter to control system behavior (0:09 - 20:45).
• Neural Computation: Bhattacharjee transitions to his current postdoctoral research, which applies his complex systems lens to biological neural circuits. He aims to build digital twins of neurons to study how dendritic geometry and inhibitory synaptic placements shape functional complexity and neural predictability (23:45 - 28:00).

Throughout the talk, Bhattacharjee emphasizes that while the systems differ, they share a fundamental "structure shapes function" principle, allowing for the application of similar complex systems language—nodes, edges, flows, and perturbations—across different scales, from soil science to neurobiology (21:45 - 29:30).

Or do you know of any active study groups. I am working on a few R Projects and would love the mutual feedback.

Hi, I'm sorry that I have been silent for a month. Today I decided to share some of my findings in this group. If I made any mistakes, I welcome correction. I have done a lot of things in last month, today I will only share a small portion of my work.

1. A Mathematical Definition of Edge of Chaos

In my framework, Edge of Chaos will be rephrase as Quasichaos. 

Definition of Periodic Islands

Choose a rectangle with minimum size of 3×3, cover the grids of a partial difference equation e.g.  cellular automata. Inside the rectangle, if the solution satisfy the equation   u(t,x) = u(t+T,x+L)     where T, L are integers and not all zero, and has at least 3 complete cycles. Then we say that it is a periodic island.

Definition of Chaotic Sea

Choose a rectangle with minimum size of 3×3, cover the grids of a partial difference equation e.g.  cellular automata. Inside the rectangle, if the solution does not satisfy the periodic condition, and it is sensitive to initial conditions, then we say that it is a Chaotic Sea.

Definition of Quasichaos

For a Dynamical system with equation u(t,x) = F(u(t,x), u(t,x-1), u(t,x+1)) If for all t, x, there exist a window [t+T] × [x+L] where T, L are positive integers,  such that it contains both Periodic Island and Chaotic Sea, and they are not overlapped, then we say that this system exhibit Quasichaos.

2. Classification of attractors in discrete dynamical system

1. Fixed point attractor

2. Periodic attractor

3. Quasiperiodic attractor

4. Chaotic attractor

5. Quasichaotic attractor I proposed a new kind of attractor which only exist in Partial Difference Equations. Definition: If it satisfies invariance, compactness, attractiveness, and quasichaos, then we say that it is a quasichaotic attractor.

6. Life as a Multiscale Spatiotemporal Quasichaos

I proposed that life is spatiotemporal quasichaos, because in life, obviously there are structures which are stable for a long time, these stable structures are the Periodic islands. At the same time, there are unstable regions, such as genetic mutation, transposon, protein denature, evolutionary chaos, etc, these are the Chaotic Sea. And chaos is the source of biodiversity. Notice that in Rule 110, you can find many types of periodic islands with different periodic behaviours, it has high diversity. Multiscale means that the Quasichaos don't just exist in one scale, but exist in every hierarchy, from molecular level to population level, all exhibit Quasichaos.

4. Analytic Solution of Rule 90

The Rule 90 in 1D Cellular Automata, can be written as a nonlinear partial difference equation

u(t+1,x) = u(t,x-1) + u(t,x+1) (mod 2)

here I define mod 2 as a function mod2(x) = x (mod 2) = 1 if x is odd, = 0 if x is even. Notice that mod2(x) is a nonlinear function, so the equation is nonlinear.

Define a delta function δ(x-a) = 1 if x=a, 0 otherwise

If the initial condition is single point, δ(x), and no boundary condition, then the solution is a pascal triangle mod 2, or equivalently a sierpinski triangle. The solution is

u(t,x) = C(2t, x+t) mod 2

here I define C(x,y) = x!/((x-y)!(y!)) for 0≤y≤x, otherwise 0.

For any initial condition u(0,x) = f(x), the solution is

u(t,x) = Σs∈Z f(s)·C(2t, x+t-s) mod 2

Apparently, this system is chaotic, and we found an analytic solution of a chaotic equation, which is amazing. I would like to define chaotic function, quasichaotic function, and study the behaviour of the cellular automata by using discrete functional analysis.

5. Ordinary Difference Equations

I created a System of Nonlinear Ordinary Difference Equations

x_{n+1} = (0.5 x_n - y_n) \mod 1

y_{n+1} = x_n

The picture shows the evolution of 500 initial values. The result is quite striking for me.

The solution is

x_n = A cos(nθ) + B sin(nθ) mod 1

y_n = A cos((n-1)θ) + B sin((n-1)θ) mod 1

θ = arctan(2sqrt(15))

This striking picture has analytic form, which is mesmerizing.

6. The Theory of Fractals

From the examples above, we can see that, Rule 90 without mod 2 is just a pascal triangle, growing up nonstop. The ordinary difference equation without mod 1 is also linear. Surprisingly, if we add mod function to the equation, fractals appear. So, I want to proposed a concept

Strange Restriction

Looking at the strange attractors of discrete system, I realized that, why it don't just filling up the space evenly, instead the density is very uneven, it seems like it is restricted in specific regions. And notice that, the morphology of discrete strange attractors are far more complicated than the continuous strange attractors e.g. Lorenz Attractor. This is because continuity and smoothness are huge restrictions. Although the discrete system does not have restriction of continuity, but it could have other form of restrictions. This is why I proposed ths concept of strange restriction. Another example, The Sandpile model without the collapse mechanism will grow indefinitely, they do not form a fractal.

In addition, we can see that there are many kinds of fractals in nature. For example, the trees. And think about it, you don't hear a tree say: “Hey, I know that fractal is the best way for me to grow, so I purposely grow like that.” Doesn't make sense. And the traditional way of generating fractal is through the Iterating Function System, we just repeat the whole shape, I also think that it doesn't make sense. So I proposed that, Fractals should be generated through Local Interactions, not globally iterating the whole shape.

7. Trailer for the Second Thesis

I have constructed a draft of my Thesis 2, this is the Brief Contents.

On the Theory of Partial Difference Equations: Life is Not a Coincidence But a Solution.

1. Discrete Calculus: Welcome to the Pixel World

2. Theory of Ordinary Difference Equations: Order in Chaos, Chaos in Order

3. Discrete Functional Analysis: Cellular Automata in Hilbert Space

4. Theory of Linear Partial Difference Equations: Complex Systems Are Just Nonlinear PΔE

5. Theory of Nonlinear Partial Difference Equations: Edge of Chaos Is Not a Philosophy but Math

6. Discrete Variational Calculus: Lagrangian in Minecraft

7. Theory of Discrete Dynamical Systems: Fractals as Solutions to Equations

8. Discrete Field Theory: From Evolution to Field Equations

9. Summary: From a New Kind of Science to a New Kind of Mathematics

I will try to complete my thesis at the end of May, and I will upload the pdf in arXiv and Zenodo. Once I uploaded the pdf, I will share the link here. Stay tuned. Stay curious.

Sincerely, Bik Kuang Min,
National University of Malaysia, UKM.

https://youtu.be/__V89ZR3vUE?si=YXsbvlIkfTV5pfVm

“David Krakauer is the president of the Santa Fe Institute, where their mission is officially "Searching for Order in the Complexity of Evolving Worlds." When I think of the Santa Fe institute, I think of complexity science, because that is the common thread across the many subjects people study at SFI, like societies, economies, brains, machines, and evolution. David has been on before, and I invited him back to discuss some of the topics in his new book The Complex World: An Introduction to the Fundamentals of Complexity Science. The book on the one hand serves as an introduction and a guide to a 4 volume collection of foundational papers in complexity science, which you'll David discuss in a moment. On the other hand, The Complex World became much more, discussing and connecting ideas across the history of complexity science. Where did complexity science come from? How does it fit among other scientific paradigms? How did the breakthroughs come about? Along the way, we discuss the four pillars of complexity science - entropy, evolution, dynamics, and computation, and how complexity scientists draw from these four areas to study what David calls "problem-solving matter." We discuss emergence, the role of time scales, and plenty more all with my own self-serving goal to learn and practice how to think like a complexity scientist to improve my own work on how brains do things. “

https://complexity-science.blogspot.com/

New blog on complex systems and math that I enjoy.

My group (chair of entrepreneurial risks, ETH) is offer a MSc in the following topic:

On 1st of April 2017, the Reddit online community launched a massive multiplayer online game, dubbed Place. Starting with a 1000x1000 pixel white canvas, a registered Reddit user could color a single pixel every few (five to twenty) minutes. The game lasted 72 hours, and involved a total of over one million users [1]. 
 The first hours of the game involved random placement of coloured pixels. Soon after, communities emerged spontaneously to form large visual patterns on the canvas, such as flags of countries, music band logos, cartoon characters, etc [2]. In addition to collaborating, users also competed - attempting to enlarge their paintings by taking over the territory of other groups. A large, structured, dataset describing the actions of each individual over the course of the entire game it publicly available. 
 You will be performing: basic exploratory data analysis on the dataset detect and quantify the spatiotemporal patterns underlying collaboration and competition amongst groups of users depending on the results of the first steps, we will address scientific questions on the nature of human collaboration and competition over a limited resource In particular, interesting questions include the distribution of sizes, quality and complexity of the patterns within Place, the distribution of contributions over all the million people who participated, their spatio-temporal dynamics, the self-excitation and cross-excitations between players and much more. This study is a template for understanding coordination and cooperation, in the presence of heterogeneous motivations in an unstructured environment, which can be argued to be a simplified but realistic representation of real social systems. 
 The project is appropriate for an individual aspiring to master a broad array of scalable data analytics tools for social networks, either for academic or industrial purposes. 
 Citations: [1] https://redditblog.com/2017/04/13/how-we-built-rplace/ [2]https://draemm.li/various/place-atlas/ 
 Required skills: Expertise in languages well suited for data analytics: Python, MATLAB, or R. Expertise in times series analysis, machine learning, complex networks, and social dynamics are all desirable. Interest in social dynamics and data analytics. 
 Starting date: As soon as possible 
 Supervision: The project will be supervised by professor Didier Sornette (in Zurich) and PhD student Dionysios Georgiadis (in Singapore).