## Welcome to the Emergent Universe WikiEdit

Welcome to the Emergent Universe. Our goal is to familiarize you with the ubiquitous concept of emergence and show you some cool examples from science and everyday life. We hope that you will find this wiki both informative and interesting.

## Emergence in a NutshellEdit

For starters, a simple definition of emergence is the idea that complex behavior can come out of relatively simple things interacting. Such a simple idea has beautiful consequences

An excellent link on this subject is the Institute for Complex Adaptive Matter's (ICAM) website Emergent Universe which is a museum showcase of emergence examples presented in a variety of ways.

## Getting StartedEdit

Check out the Science Hub, Games Hub, Nature/Environment Hub, or Other Hub to access lists of available articles.

To see our design philosophy go here.

For a quick list of great emergence resources on the web go here. And for information on emergence in book form go here.

## A More Detailed Explanation of EmergenceEdit

One way of looking at Emergence would be to try to relate it to the complexity in a system.

Emergent systems seem to depend on four factors:

- the concentration of the interacting particles
- the nature of the interactions
- the flow of energy through the system
- and finally, the cycling of that energy flow

Regarding concentration of particles, typically we see that below a certain critical concentration, there is no emerging pattern or complexity. If we increase the concentration of particles in the system above that critical value, we see an increase in complexity. *But,* if we increase the concetration above an upper critical concentration, the patterns die out and entropy dominates the system. This careful domain of increased complexity or interesting activity is referred to in some fields as an energy landscape.

A precise or quantitative measure of complexity itself can be highly subjective, but we can try to borrow a bit from information theory to help us craft a very general mathematical relationship for the complexity of a system.

If we define generally $ C $ as complexity, $ n $ as the number of interacting particles, $ i $ as the degree of the interconnectivity of the particles, and $ \nabla E(t) $ as the time varying energy flow through the system, then we can say $ C \leq f [n, i, \nabla E(t)] $

where $ f $ is a function that depends on the system. In case there is any confusion, all this equation really does is restate those four factors mentioned earlier, but in a compact mathematical format.

Another way of trying to think about Emergent systems might be through the context of thermodynamics- particularly the second law- and self-organizing systems.