One important aspect of Complexity Science is the idea of “emergence” or “self-organization,” where simple rules or circumstances lead to events that are not scripted. In other words, where things seem to take on “a life of their own.” The iOS Apps Life Game Touch and LifeGameHD speeder do a good job of demonstrating the cellular automation “game,” Conway’s Game of Life.
Genetic Galaxy Defender is a simple space shooter game written in Flash where you play a heroic space pilot defending your motherland from the horde of invading alien robots (that, for some reason, look like Octopi). This is a game I made for a final project in a Systems Engineering class where we focused on biological inspiration in engineering design.
Behind anything that is truly complex there are simple rule sets. This video includes demonstrations of cymatics, which is the visualization of sound waves.
If you take a purely determinate function and iterate it over time difficult-to-predict behavior can emerge. If you only use the same function, then the outcome is easily determined and therefore not complex. But if you use more than one determinate function or a set of rules with simple determinate functions then difficult-to-predict behavior may emerge.