Emergence is one of those terms that is easy to start thinking about but is quite hard to pin down exactly. The generally accepted idea is of some phenomena or behaviour that "emerges" from a complex system in an unanticipated manner. As our understanding of complex systems grows however, we may decide that some phenomena are in fact expected after all, and are no longer mysteriously emergent. A useful and pragmatic definition of emergent phenomena are: those phenomena exhibited by a system that are unexpected a priori, based on the input parameters or information we put into a model or system. This is particularly pertinent to simulated systems for which we can and do formulate a microscopic model, and from which some unanticipated macroscopic phenomena emerges.
Emergence and Complex Systems have become topics of interest in recent years and are described with various degrees of success in several popular science books. Some of my favourite books in this area are:
The study of emergence in the context of simulation models involves finding ways of usefully identifying, classifying and preferably quantifying phenomena we might describe as emergent. We generally need to formulate a microscopic model system analytically, and try to implement or code it up as an efficient simulation. We then need to figure out what to measure or observe so we can capture any emergence. Sometimes this is very surprising indeed and we need to think up unusual things to measure from the overall system. There are techniques from condensed matter physics that are useful in analysing spatial structure and phase transitional emergent phenomena. Often we need to thoroughly investigate different initial model conditions and perhaps try to measure some macroscopic property over many different microscopic runs of our model system. Visualising the overall system is a great aid to deciding what is worth measuring in a model, and various rendering technologies can be used to give a static or animated picture of the system.
One emergent phenomena we have found is in our artificial life model. This is a microscopically formulated predator-prey model of semi-intelligent animat agents. These simulated "animals" interact in a spatial environment according to rather simple built-in rules. We expected to find growing clumps and the obvious sorts of simple and random shapes in a simulation. The spiral pattern and various spontaneous formations reminiscent of military attack and defence formations emerged. The image top right shows an emergent spiral of red predators and blue prey against a background of green corpses. Read more about these emergent spirals in the ALIFE project pages and Technical Notes: CSTN-007, CSTN-009, CSTN-010, CSTN-015 and CSTN-017.