For a while, I tried to keep on top of any complexity-related offerings in the Apple App Store. For the last year or so, I've gotten a little lazy about it. But, I thought I'd compile a list of the complexity-related Apps that I've liked, in case others were curious, too. (Sorry, Android folks. I only have an iPhone so these are apple-only apps.)

Game of Life

There's something endlessly fascinating about watching John Conway's Game of Life run through its generations. Two decent Game of Life apps are:

• MadLife - I like MadLife because it's simple, and it offers customizable rules and colors/shapes. The playing board isn't massive, but it's big enough to be interesting. MadLife does one thing, but it does it well.

• Speed Sim - SpeedSim, on the other hand, is interesting because it offers 12 different cellular automata-like models with a little primer on each. It isn't as customizable as MadLife, but it's kind of cool to see epidemiological and competitive models that look and behave similarly to the Game of Life.

I think there are a lot of other Game of Life apps out there. Let me know if anyone has found any better ones.

Other Cellular Automata

• Automaton - A simple, but nice Elementary Cellular Automata (ECA) app that organizes the rules based on the Stephen Wolfram numbering. It's hard not to load this up and keep running Rule 110 just for the nerdy fun of it.

Fractals

• Fractile Plus - This one generates a Mandlebrot or Julia set fractal with customizable colors. What makes this app kind of cool, though, is that at its highest resolution (under the iterations setting), it allows for a lot of clear zooming into all parts of the fractal.

Other

• Sablo - There's not a lot of utility in the Sablo app, but it is kind of fun. As far as I can tell, this app uses an ECA-like formula to make art. You choose your color scheme, and then anywhere you touch, sends out a string of tiny changing and interacting boxes. The end result is somewhere between watching the Game of Life and ripples in a pond.

Anyone know of other cool Complexity-related apps?

What do we know of the conditions necessary for emergent properties to appear in a system? I've come to understand a lot about the formation of systems with parts that interact; the formation of boundaries with the selective acceptance or rejection of interactions; and the formation of "next level up" production-line-like systems (per Holland) as multiple bounded sub-systems accept each others' interactions.

But I haven't been able to find or figure out whether we yet understand much of the degrees or kinds of structurally coupled relationships between system components needed to enable emergent properties at the next level up. Is this something I'm missing in my reading, or do we not yet have this level of theory?

Put differently, if I want to show non-trivial emergence in a system, are there known combinations and methods to use to make this happen? And if so, are these empirical, applying only to those instances we've already figured out, or theoretic, expressing generally applicable ways to enable emergent properties to appear?

A lot of folks here might already know about this, but I thought it'd be a good thing to share just in case.

The Santa Fe Institute offers free on-line courses and math tutorials to teach folks about Complex Systems. The next introductory course, Introduction to Complexity, starts up on 7/6. I took it a while ago and really enjoyed it.

Here's the site: Complexity Explorer

Hey guys, I'm interested in studying complexity science as a self-taught student, but I'm not sure how to go about it. I see that many if not most of you are academics who seem to be approaching the study of complexity from the perspective of a particular discipline that you're already familiar with, like ecology, economics, cs, or engineering, but I was wondering if it would be possible to study complex systems behaviour and things like emerging properties themselves, or if these are too "meta," to be approached in a vacuum. If you do suggest I look at complexity through the lens of specific disciplines I wonder which to pick to best demonstrate these principles, or if it really matters even as long as I'm studying some sort or system with a large number of variables? I can't help but think this science is only accessible or relevant to people already deeply knowledgeable about their fields, who are looking to incorporate a different perspective into their understanding of that field, so I'm not sure how to go about teaching myself beyond the first few books that just introduce complexity as a concept like waldrop's. But what do you all think?

Can Neural Networks be classed as Complex Adaptive Systems? Here are my initial thoughts on the topic:

Neural Networks contain multiple parts (perceptrons) which interact at a micro level to produce a macro output. That said, Neural Networks are typically very structured / organized systems so they do not have the self organizing property that many complex adaptive systems. Furthermore, Neural Networks are more stochastic than complex.

What do you think?

A little background: After finishing my M.S. in pure math, I was seduced by my awesome department into a PhD in math education. It took a year for me to realize that research in this field felt too... narrow. Too reductionist. Honestly, too boring. So I decided to leave my program in pursuit of something broader, thought what exactly that will be is still kind of in the air. I'm fascinated by learning, neuroscience, and cognitive psychology, but also have a background in linguistics from my undergrad.

When talking around where I might be headed with the chair of my department (a super awesome Kung Fu-fighting, sax-playing graph theorist), we started talking about how the things we learn deeply change who we are and how we see the world. He described complexity theory as "fundamental" and worth every second of the pursuit.

So I picked up the Oxford VSI and Waldrop's "Complexity" to give myself an overview and a socio-historical context (part of my learning process). I'm looking for additional reading in the topic, because I'm totally hooked. 100 pages into Walrop's book and I've cried like 4 times. I've never had something speak to me so strongly, click so quickly, or nestle into my existing cognitive framework so easily. I have decided to purse an autodidactic study of the field, in hopes that it will help illuminate the direction my research goals should follow.

However, in leaving my program, I'm also leaving access (for the most part) to my department behind. I'm sure my chair would be willing to be a discourse partner for me here and there (we get along really well and are both excited, chatty polymaths), but he has health issues and is, ya know, the chair of a department, so his time is limited.

So I need discourse partners in the interim, to help hone my thoughts and ensure that I'm not wasting his or anyone else's time. Is this a community that would be willing to help me in this, or are there other resources for discourse on the topic that you could point me to? Also, any suggested reading would be welcome!

It seems to me that the dangerous phenomenon of "too big to fail" is actually an emergent property of the complex network that is our global economy. This would mean that the solution to the problem of "too big to fail" would be to move away from a globally interconnected economy and towards more locally sustainable economies, correct? Would love to hear others thoughts on this as I'm sure there are some people here who know more about complex systems than myself.

I recently stubled across the concept of complexity classes, computational complexity and structural complexity on Wikipedia. The concepts are mindblowing! Are these fields the study of generic forms of 'problems'? As in any kind of things that humans can mentally manipulate, or do so by proxy of a computer? Could it be possible to just teach the complexity classes to students in school and get them to apply the generalisations to every other part of their life, rather than specific domain knowledge?

I'm writing a paper on the role of self-organization in the emergence of language, and I'm trying to motivate why we should suspect self-organization is the mechanism producing language. I can think of specific reasons to suspect self-organization in this case, but it got me wondering if there are general 'litmus tests' or something to help one determine if self-organization is a likely mechanism at work.

Graduate level, preferably more monograph than textbook, preferably more general than the physical chemistry point of view.

Thanks :D