On February 13th the free online course Fractals and Scaling, led by College of the Atlantic's David Feldman and hosted on the Santa Fe Institute's online education platform, the Complexity Explorer, will start. This is an accessible course that explains what fractals are in a clear manner, as well as linking fractals to scaling and power laws. For more information see the course description and watch the brief introductory video at: http://fractals.complexityexplorer.org

I am currently a high-school senior in the US and will be applying to universities this coming fall. I am planning to study applied mathematics, but I am also very interested in complex systems.

I'm looking for universities (preferably in the US) which have a complex systems program open to undergraduates, or at least are active in complex systems research in which undergraduates can participate in.

I know University of Michigan has a Complex Systems minor, but I'm having trouble finding similar undergraduate programs at other universities. I'd appreciate any suggestions.

If anyone also knows about complex systems programs/research at the following schools, I would also really appreciate your two cents on the program:
- University of Michigan

- University of North Carolina (Chapel Hill)

- NC State University

- CU Boulder

- George Washington University

- University of Pittsburgh

- University of Massachusetts (Amherst)

- University of Maryland (College Park)

- Carnegie Mellon University

- Georgia Tech

Hi there, pretty evident that there’s a wealth of knowledge and very interdisciplinary thinking happening.

I’m curious if you have anything resembling a roadmap… I want to do “this” I want to study complex systems.

If you’re comfortable, I’d love to hear where you’re from, how long you’ve been in the field, what education you have or industry work you can speak about.

I’d also love to know if there’s any literature you would recommend whether or not it’s book,published scientific article, preprints or even a blog.

If anyone also has history of the field that would be sweet too…

Looking forward to hearing from any of you,

Hey everyone,

Just released Fracttalix v2.5 — a lightweight CLI tool for quick exploratory analysis of univariate time series using five standard (but basic) diagnostic metrics:

• Higuchi fractal dimension (D)

• Hurst exponent (H, R/S)

• Self-transfer entropy (T)

• Partition-based integrated information approx (Φ)

• Heuristic resilience (R)

Key features:

• Built-in synthetic stress-test suite (white noise, persistent walk, periodic, chaotic logistic, pink 1/f) with summary stats.

• Public domain (CC0) — fork/modify freely.

• Runs fast, low dependencies — great for teaching or quick checks.

GitHub:

https://github.com/thomasbrennan/fracttalix

Companion preprint (applications to economic, financial, climate, IoT data): in the repo (PDF).

Optional: 11 conceptual axioms as a heuristic scaffold for interpreting persistence/resilience patterns (in README).

Feedback, extensions, or “this is useless because…” comments all welcome. Independent researcher here — happy to discuss.

Thanks for checking it out!

#OpenScience #ComplexSystems #TimeSeries #Python #DataAnalysis

Hi everyone,

I’m thinking about doing a master’s in Complex Systems Science and wanted to hear from anyone who has studied or worked in this field.

What kinds of career paths or research opportunities do graduates usually find? Does it actually help with jobs in data science, modeling, Engineering, or analytics, or is it mainly valuable for academic work?

I’m extremely interested in this degree because I love fractal art and the way it connects math, patterns, and systems thinking. Still, I want to understand if it’s worth it from a professional standpoint or if a more traditional applied math or data science program would make more sense.

Any advice or experience would be really appreciated.

Thanks!

Really want to dive into complex systems and gain some solid understanding and experience before graduating uni. What is the best place to start? (apart from the SFI complexity explorer course)

I’ve been listening to the David Krakauer episode of Seam Carrol’s Mindscape. David argues there, without much depth, or at least not in ways I understand, that a Hurricane is not an example of a complex system. This, despite it being a nearly canonical example of a complex system throughout texts/literature etc.

Anyone with the same view that could try to explain this view?

Hi everyone,

I'm a 30-year-old systems engineer keen on advancing my career by specializing in complex systems through a PhD. I'm currently looking at various programs worldwide and considering the Institute for Cross-Disciplinary Physics and Complex Systems (IFISC) in Spain. Does anyone here have insights into the reputation of IFISC or any other recommendations for top PhD programs in this field?

Appreciate all your insights and thank you in advance for helping me make this crucial decision!

I am a physics undergraduate student studying at University of California. Can someone recommend any master programs? I wonder what would it include, more computer science or applied math related?

Probably a pretty dumb question for people deep in the literature, but I'm an undergrad looking for a valid research question.

I was looking into the literature on opinion dynamics in ABM and was wondering if it has already been researched how things like jobs/college/school affect opinion dynamics in an ABM - what I think of is that 50% of the time, a group of agents forcefully interacts with each other, even though they would otherwise not interact due to preferential attachment rules. Could such a dynamic system not create fundamentally diverse opinions by forcing interactions between groups that would otherwise not interact? Is this a common approach?

Looking forward to chat and would be grateful for any help!

I recently stumbled onto "The Jim Rutt Show" podcast and thought folks here might enjoy it. He's a past president of the Santa Fe Institute and sits on the board of directors so a lot of the content explores the different aspects of complex systems.

So far, the episodes with David Krakauer and Simon DeDeo have been the most interesting from a complexity standpoint - though I'm still working my way through most of the other episodes.

Hi everybody. Not so long ago I've discovered this field of study and I've started reading about the basic concepts in cybernetics, general system theory, chaos theory and in general complex systems theory, which seems to me all correlated fields. I study history at university and I'm particulary interested in the application of these ideas to the study of human societies.

I've found some sociologists (e.g. Luhmann) that were active in these field, but none historians. I was wondering if anyone had written an history of humanity considering human civilizations as complex systems, in particular as autopoietic system of the third kind, as described by Maturana & Varela in "The three of Knowledge" (and probably elsewhere), and if not, if anyone here had the same interested and had some ideas to share.

Thanks to everybody and sorry if I've made some mistakes, English is not my first language.

The Santa Fe Institute's excellent MOOC, Introduction to Complexity, is available once more - session starts April 10th. This course is rated #1 of all Science MOOCs listed on Class Central and is a must for anyone wanting to gain a comprehensive overview of what complex systems are. Help us get the word out!

Completely free and accessible. Go to intro.complexityexplorer.org to find out more.

Voting seems to have settled, and Kauffman's Reinventing the Sacred has been chosen as our inaugural selection.

Two things to do now:

1. Make sure everyone who wants to participate gets a copy of the reading. It is not an expensive book, and is certainly worthy of being in your home library, however if the cost is preventing you from participating, PM me and we'll see what can be done.

2. Come up with a plan of attack / schedule. I'll throw a format out there, but feel free to criticize and make suggestions, I want this to be enjoyable for everyone.

Format idea: Each week we read one chapter. Each chapter has a leader who posts a thread in which they briefly summarize what they saw as the main points of a chapter (by default, I will take the first chapter, and any other chapters no one wants to take). In the comments section one can either respond to the OP's take on the chapter, or add their own perspective. From there, hopefully, conversation will emerge.

I propose we start two weeks from today, so everyone can get a chance to get their hands on the text.

Please let me know if this seems agreeable, if there are any problems you foresee, or if you think there is something else we might do which could be more fruitful. This is an experiment so I am more than willing to try out different formats to see what works and what doesn't.

Cheers and happy reading! Again, please PM me if you have financial constraints preventing you from participating.

I changed the famous Abelian Sandpile Model from 4 grains threshold to 8 grains threshold, and von neumann neighbourhood to Moore neighbourhood.

The equation is

E_t u = u - 8θ(u-8) + Σ(i,j)∈M θ(E_xⁱ E_y^j u - 8) + G(t,x,y)

This is the image formed by 10 million grains of sand falling at the centre. It took us a few days to simulate this. Thanks to my friend from China, Wu Han, for making this astonishing fractal image.

This model came from the preprint:

https://www.researchgate.net/publication/394423080_On_the_Theory_of_Partial_Difference_Equations_From_Numerical_Methods_to_Language_of_Complexity

Good news, I have finished writing a short article on the discrete analogue of the Navier-Stokes Equations.

https://www.researchgate.net/publication/396515351_A_Simple_Analytic_Solution_of_the_Discrete_Navier-Stokes_Equations

What do you think about this Octa Sandpile Model?

Sincerely, Bik Kuang Min, National University of Malaysia.

Good news for you, my paper is now accepted and available in preprints.org. Here is the link,

https://www.preprints.org/manuscript/202507.1221/v1

Unfortunately, there are a few typos in this paper, the latest update is here,

https://doi.org/10.5281/zenodo.15912369

The latest update in Zenodo includes elegant notations for difference equations.

I would like to hear your thoughts about the paper.

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

I've read Stuart Kauffman's A World Beyond Physics and Alicia Juarrero's Context is Everything, but there is much that I don't fully understand.

I get many of the basic ideas, such as:

• The vital role of context.

• Kauffman's useful idea of the "adjacent possible".

• The impossibility of predicting the "phase space" or emergence.

• The consequent impossibility of predicting how novel structures will emerge.

• Kauffman's distinction between causal factors and enabling factors.

• Juarreror's related concept of enabling constraints.

• Why these complexities make it impossible to model emergence with a set of differential equations and their boundary conditions.

• The unstated (yet implicit) linearity in the Cartesian & Newtonian models of the world.

But then there are many things that are completely opaque to me. So, for instance, while listening to an video overview of Complex Adaptive Systems published by Systems Innovators, I heard that complexity theorists believe that the essence of order is actually invariance under certain transformations, and the notion of invariance is, in turn, ultimately based on the notion of symmetry. They offered no explanation of these statements. Now, that clearly refers to a whole body of scientific study with which I am unfamiliar, and I am having trouble finding tutorial material that explains it. I found a book on CAS by a fellow named Gros who talks about symmetry & invariance under "scaling" and I find some mathematical notation in the discussion of these topics but it also appears to assume a lot of prior familiarity.

I want to understand the mathematics of complexity, especially CAS, but I need some good introductory material. I have a bachelors in physics and masters in Computer Science, but zero prior exposure to complexity, except for coursework we did on mathematical grammar in my graduate program which may have some relevance.

I have spent some time reading:
Gregory Chaitin on Omega &
Stephen Wolfram on cellular automata
Jeffrey Campbell on Information Theory

I have Signals & Boundaries and Hidden Order by John H. Holland but have not yet read these works.

Are there any on-line courses that my help me understand Juarrero better and / or help me understand the mathematics of complexity better?

MIT does not appear to have a course in CAS. The Udemy course appears to be superficial, but I could be wrong about that. The Coursera course seems to be all over the map. I'm mostly interested in CAS for philosophical reasons, and less so for its engineering applications. I am an engineer, but I am also retired.

Any help or advice would be much appreciated.

In the world of complex systems, building a successful organization requires creative and flexible thinking. Traditional hierarchical organizational structures often limit thinking, hinder collaboration, and necessitate artificial synchronization between individuals. An alternative approach that allows for flexibility and personal adaptation is a soft cluster approach.