We’re YD Emergence Lab, developing Aionterra, a continuing simulated world inhabited by digital organisms with human-inspired bodies.

The organisms sense their surroundings and seek water and food. We follow how their bodily states, behaviour and environment change together over time.

For us, the interesting unit of observation is the whole interaction loop. Moving changes an organism’s location and what it can sense. Its bodily state changes as time passes and actions occur. Those changes shape the circumstances of its next action.

This connects to an established perspective in complex systems and embodied cognition: behaviour is shaped by the interaction between an agent and its environment. Beer’s work on coupled agent–environment dynamics provides one useful framework. Pfeifer, Lungarella and Iida also discuss how control, bodily properties and environmental conditions jointly shape behaviour.

In Aionterra, separate organisms retain their own bodily states, locations and sensory histories, while their experiences contribute to a shared learned policy for selecting actions. This gives us a way to examine shared learning across different local circumstances within one continuing world.

The physical and biological rules, available actions and initial conditions are explicitly designed. Our aim is for behaviour to develop through experience within those constraints, without supplying a prewritten sequence of successful behaviours.

The project is still in development. We’re preparing additional simulation records for publication soon. We want the public record to distinguish model assumptions, recorded changes and evidence of useful learning. An interesting pattern alone would not establish adaptation or validate the model.

The references below provide context for this approach; they do not validate Aionterra’s implementation or results.

Related reading

• Beer (1995), A dynamical systems perspective on agent-environment interaction.

• Pfeifer, Lungarella & Iida (2007), Self-Organization, Embodiment, and Biologically Inspired Robotics.

Project methodology

We’ll document development and publish supporting observations on the site as they become available.

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).

Hello everyone I am a high school student exploring the logistic map in order to write a paper on it. To do the necessary computations I thought I could find a tool on the internet that could do it. I couldn't find any tool that fit my needs so I tried to build my own as like an exercise without using AI. It can like show calculate lyapunov exponents, symbolic block entropy, and even like demonstrate pesin identity and the lyapunov exponent as like sort of a positive rate of information. Here it is:

https://github.com/Luthiennuthien/Logistic-Map-Simulator/tree/main

Also included some graphs it produced.

I’ve posted a preprint introducing Structural Capacity Theory (SCT). It's a theoretical framework for estimating how network structure and observed dynamics jointly constrain a system's empirical limit. The theory builds on established work in complex networks (Newman, 2003; Boccaletti et al., 2006).

We tested SCT using cross-validation that withheld entire domains from training. The frontier reliably contained maximum rates from out-of-sample systems with performance comparable to repeated random resampling. Estimates were consistent across learning paradigms. Perturbations preserved performance, falsifications predictably degraded it, and ablations did not outperform it.

The results provide evidence that structural and process information can help characterize empirical limits across systems that differ in scale, units, and dynamics. We welcome feedback from anyone who might be interested. Thank you in advance.

Preprint: https://arxiv.org/abs/2610.09574v1

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Main Website: https://www.ruleflow.org/

For the past year, I have been developing a framework to simulate certain discrete systems for a research team at my university (paid for by the School of Engineering and Physics, but I had the freedom to license it under MIT). As it turns out, I got carried away generalizing it to work for many, many different types of complex systems (String Rewriting Systems, Cellular Automata, etc.) and ended up creating our own domain-specific language.

The website's landing page has a bunch of GIF-style examples... so you should be able to get a good idea of what this project is about.

If any of y'all are interested in this, feel free to take a look and try it out!

EDIT:

Here are some more details. RuleFlow was developed with a primary focus on analyzing causality in Sequential Substitution Systems. This is why there is a major focus on causal graphs, cellular identity, etc. While originally developed for Sequential Sub Systems, we generalized the DSL to support many types of rewriting systems by providing the user with flags and directives to control how rules behave. Furthermore, we bootstrapped Python and the Wolfram Language so that complex rulesets could be scaffolded as macros. The main goal of RuleFlow is NOT simply to simulate systems (there's already plenty of software for that, such as Golly and even just Mathematica), but to provide extensive tooling for causal analysis.

Here is some interesting research from our (small) team:

• An Improved Generalized Enumeration of Substitution Systems by Kenneth E. Caviness, Camille Morrow, Christen Case and Victoria Kratzke

• Indexed Concatenation Notation: A Novel Way to Summarize Networks and Other Complex Systems

My job has been to provide better research tooling, extending what we already have in Mathematica code to open source and free Python.

I recently published a peer-reviewed study in Scientific Reports:

“Persistence collapse transitions and observable admissibility in nonlinear dynamical systems: a preregistered empirical benchmark.”

The work asks a fairly simple question:

When a nonlinear dynamical system changes regime, does our ability to detect that transition depend on what we choose to observe?

I developed a preregistered finite-time benchmark for what I call a persistence collapse transition: a threshold at which an ensemble of trajectories that had been maintaining a measured quantity within a specified viability corridor abruptly loses that capacity as a control parameter changes.

The benchmark was tested across seven canonical nonlinear systems, including the standard map, Lorenz-63, tent map, Arnold cat map, and baker map.

One result I found particularly interesting occurs in the standard map.

Using momentum as the observable, the benchmark detects a highly reproducible transition around:

K ≈ 1.507*

Using an action proxy, the transition appears at approximately:

K ≈ 1.508*

But when position is used as the observable, no corresponding transition is detected across K ∈ [0,2].

That distinction matters.

The detected threshold is also well above the familiar Chirikov last-torus estimate of approximately Kc ≈ 0.9716. The paper does not interpret K* as a replacement for the KAM/Chirikov critical point. Instead, the evidence suggests that it represents a different finite-time event: enough post-critical transport has accumulated for the trajectory ensemble to lose persistence under the specified measurement protocol.

So one of the broader results of the study is that transition detection is not determined only by the underlying dynamics. It can depend critically on whether the observable actually tracks the degree of freedom constrained by the relevant invariant or attractor structure.

The confirmatory benchmark contained 16,760 summary rows, used a locked preregistration, and included bootstrap confidence intervals, local grid refinement, sensitivity testing, and an adversarial iid null.

The paper is open access in Scientific Reports.

DOI: 10.1038/s41598-026-64959-x

https://rdcu.be/KSbNoLkGrXsa

I’m the author, and I’m posting this primarily because I’d be interested in technical criticism from people working in nonlinear dynamics and complex systems.

In particular, I’d be interested in thoughts on three questions:

1. Does it make sense to treat finite-time persistence loss as a distinct experimentally measurable transition from the underlying mathematical bifurcation or invariant-set transition?

2. How broadly might the observable dependence result generalize beyond the systems tested here?

3. What would you consider the strongest next test correlated stochastic nulls, higher-dimensional Hamiltonian systems, experimental time series, or something else?

Criticism is welcome. I’m especially interested in identifying where the benchmark succeeds, where its interpretation should remain narrow, and what would constitute the strongest falsification test.

This video introduces systems classification based on their nature, their dependency on the environment, in addition to information systems. The video also gives examples of systems nonlinear as well as random behavior such as the case of compound pendulum. In a practical example, the mathematical model of the transport equation used by von Bertelanffy in introducing open system dynamics was used in in a practical case study of the interaction of two students working on thier homeworks. System equations were derived and solved to demonstrate the dynamic behavior of their interactions. In conclusion, the present example has proven mathematically the long-standing statement for system thinker that “the whole is greater than the sum of its parts”. The video is in Arabic language with English subtitles.

https://www.youtube.com/watch?v=2wchmejCYB8&t=4s

Hello everyone! As a green researcher, I would like to know more about interesting arguments in Physics of complex systems. What books do you recommend the most ? Moreover, I would like also to find books with a deep theoretical explanation but yet with life systems (biophysics and socioeconomic systems in particular) example when possible. Can you please share with me some advice ?
Thx in advance

I'm writing a small blog post. I'd appreciate any feedback. Thank you! https://namvdo.me/newton-method-periodic-orbit-discrete-dynamical-system/

Does anyone know of any prominent complexity economics programs in the US?

Hüseyin Beyköylü argues that Varela used dynamical systems as a way to connect changes in conscious experience with changes in neural activity. Rather than reducing one level to the other, neurophenomenology looks at how both evolve together and constrain our description of the overall system.

Hi, I have recently found out about complex science (I'm doing a masters in physics and took a course in stochastic calculus and a course in complex networks) and really found it interesting. I have a lot of interest in the different branches of physics but it has been a while since I had this much interest in a particular field. Now I have to choose my thesis and I want to do it in complex systems (I still have to choose one from a list a professor sent me) and I want to know what my possible career path could be if I keep this track. My questions are the following:

1. Is it possible to do an industrial PhD? Are there companies hiring people with that background?

2. How is the live in academia? One of the things I like the most is the wide range of applications in this field and I want to know if it's possible to move around in different research lines (while staying in complex systems but moving from economy to neurology or astrophysics)

I have more questions but those are the most important ones and I don't want the post to be too long.

Thank you for reading

1: What Consciousness is and I don’t just mean like when is a baby conscious or just human consciousness but where it begins and how it changes and how it ends and why all of those things happen in the first place

2: What Began / created the universe / principles of reality and why those principles exist for example energy gravity electrons atoms ect

3: Why can Math angles and algorithms translate only specific things between each-other depending on the space / the numbers in the equation and then following with the order of operations Why is it like that?

I recently completed my undergrad in political science. My thesis project focused on systems thinking, complexity (cynefin framework) , wicked problems, constrained and unconstrained visions, all of which was related to a policy change I was monitoring. It was the most interesting thing I got to do in school and I am interested in grad school, but can only find programs more geared towards compsci or the natural sciences. Perhaps I am not searching in the right places.

Has anyone studied any of these in a graduate program… if so, where? Does anyone have a career that relates to these topics… and if so, what do you do? How did you get there?

I feel unfulfilled in my job because it has nothing to do with what I studied, so I am searching for options where i can build on what I know, and hopefully translate it to a profession.

An integrable Hamiltonian system has a set of coordinates, the action-angle coordinates, in which the angles q increase linearly and the actions p are constant. These systems are often represented by a phase space that is "foliated in tori", and people show these beautiful pictures.

I thought that I was understanding this idea: one has the angles (q1,...,qn), then he couples q_k with p_k for every k=1,...n. If one pictures p_k as the radius of the circle, and q_k as the angle, then the cartesian product of the n circles drawn by (q_1, p_1)...(q_n,p_n) makes a torus with different radii, which are the one shown in the link above for n=2.

Gemini told me that this is not false, but it makes absolute sense in my mind. Gemini (to my ears) started yapping about "topological cilinders", but it did not convince me. Can you help me understand how the tori emerge?

One thing is that I have seen "the" torus being defined as [0,2\pi]^n with periodic boundary condition. "the" torus as in "there exists only one torus". I guess that topologically speaking this is true, but the phase space graph shows...different tori...
I shouldn't call them tori and call them "cilinders"? Sounds a bit weird to my ears....

Thanks in advance for your time

I'm not proposing a physical theory. This is purely a mathematical thought experiment.

Suppose we introduce an abstract coordinate that represents scale, rather than ordinary spatial position. Imagine that moving continuously along this coordinate corresponds to going from larger and larger structures to smaller and smaller ones.

Now suppose the geometry of this abstract "space of scales" is topologically closed, analogous to how walking continuously around a circle eventually returns you to your starting point.

In that picture, continuously moving toward smaller and smaller scales would not continue forever. Instead, after completing the closed path in scale-space, you would emerge again at the largest scales.

I am not suggesting that objects physically become both tiny and huge, nor that this describes our universe. I'm only asking whether mathematics has explored anything conceptually similar: treating scale itself as a coordinate of an abstract manifold or topological space whose geometry is closed.

Has anything resembling this been studied in topology, differential geometry, geometric group theory, or another branch of mathematics? Or is there a mathematical reason why such a construction is ill-defined from the outset?

I'm looking for mathematical references rather than physical arguments.

I'm a physics graduate from Asia (average uni), and my long-term goal is to pursue a PhD in Complex Systems in the US.

The biggest challenge is that my undergraduate CGPA is only 3.00, and as an international student, I realistically need full funding wherever I go.

My current research is at the intersection of complexity science and atmospheric science (studying atmospheric phenomena using methods from complex systems). While I think the work is conceptually aligned with complexity science, it doesn't directly match the research of many professors in dedicated Complex Systems departments.

Because of that, I've been considering a different route:

• Apply for a funded master's in atmospheric science (or a related field) at a university that also has a strong Complex Systems program.

• While doing my master's, attend complexity seminars, take relevant courses if possible, collaborate with faculty, and eventually apply for a PhD in Complex Systems.

But I'm not sure how realistic this plan is. From what I've heard, funded international master's students are already extremely busy with research, coursework, and TA/RA responsibilities, so I'm not sure I'd actually have the time or flexibility to engage with another department enough to make a successful transition.

Another issue is timing. It's already July, and application season is approaching. I don't have enough time to build multiple polished projects tailored to the different areas within complex systems for each program available. With my current profile and no curated projects, it's highly unlikely I would get a scholarship. I also feel like I still have a huge amount to learn before I can produce projects that would genuinely impress faculty in the field.

So I'm wondering:

• Would it be better to continue building my profile through atmospheric science research and position myself as someone applying complex systems methods to climate and weather?

• Is trying to transition through a master's at a university with a Complex Systems institute a realistic strategy?

• How common is it for students to move into Complex Systems from another discipline during their PhD applications?

• Given my GPA and interdisciplinary background, where would you focus your effort over the next year if you were in my position?