It is understandable why when people see complexity they imagine their needs to be some designer behind all of it. Consider the computer. The computer is very complex with all of its components. The computer had a designer behind it, a mind, that knew exactly what it was doing to put all the pieces of a computer together. Or consider an orchestra. All those instruments come together to produce complex music. There is a designer behind all of it, namely the conductor. The conductor gives instructions to the orchestra and they follow through thereby producing music. It therefore makes sense to us when we see something which is complex we imagine that there needs to be some designer behind all of it. This kind of complexity is known as "top-down complexity". There is someone on top who transmits the information down below, the one on top is the designer, the one who created the complexity.
Now consider Conway's "Game of Life". The Game of Life is a computer simulation developed by the mathematician Conway, still living. It is a very simple game. It consists of a grid with each square either on or off. It follows very basic rules. If a square is isolated by itself, lonely, it will sadly die out (turn off), if a square is near another square, they will have sex and reproduce another square (turn on). If there are too many squares next to one another, they have an overpopulation problem, and some will die out (turn off). These are not the specific rules but just enough to tell you the idea of this game. What is interesting is that certain arrangement of squares will produce some very complex patterns. Sometimes it creates simulations as if their is a living organism, for example see this this. The Game of Life is an example of "bottom-up complexity". There is no designer in the Game of Life. There is no programmer who is making this simulation run. It runs by itself. The squares follow a few basic rules of life and when these squares get together they creates a complex pattern.
This is what emergent complexity is all about. The idea that complexity can emerge from bottom-up components that follow very few basic rules. Emergent complexity is not uncommon, on the contrary, it is all around us. Consider walking in New York City. It does not have to be New York it can be any place which has many people walking in the streets. If you look at the movement of people from a bird's eye view, from high above, you would see a pattern emerge. You will see a direction of movement one way and another direction of movement in the opposite way, these two directions will never cross each other. One might imagine that there is some designer behind the movement of people which produces these patterns if he sees this complexity but that is not the case. There is no designer in the movement of people. The complexity emerges from bottom-up based on a few basic rules of human movement. These rules are so basic that most people do it on a subconscious level. The first rule is that people follow the person in front of them, the idea is that if there is a person walking already in front then there is nothing in your way to stop you from walking ahead, so we naturally follow the person ahead of us. The second rule is that we never get too far back from the leading person, lest someone else, from another direction, can get in the way. The third rule is that we never get to close to the person in front of us. These simple rules, when put together, just like the Game of Life, produces some complexity, not very complicated, but there are patterns nonetheless that direction motion of people. You see even more complicated patterns emerges when bird fly together. They stay together and operate, if seen from far away, as some giant intelligent organism. The formation of bird flying is also the result of emergent complexity. There is no leader bird. Rather they follow some basic rules. Do not get too far away, do not get too close, fly away from danger, and so forth. None of these birds imagines itself to be making intelligent choices to create this complexity, it happens naturally. Likewise, as with the New York example none of the people imagine themselves to be making an intelligent choice to create flow complexity, it happens naturally based on the simple rules of the components.
Perhaps the finest illustration of emergent complexity is evolution. We have incredibly complex species of animals. Millions and maybe even billions of different kind of species. Where did they all come from? All of them are so many times more complex than the most advanced computer we can build. We might imagine that there had to be a central designer behind all of this life (God). And this was the common held view. But it turns out as we know today that all the life around us was not centrally designed, it emerged from bottom-up. Life follows a few basic rules that everyone would accept. First, offspring have variation from the parents. Second, parents pass most of their traits down to the offspring. Third, the traits most capable of surviving in an environment are more likely to be passed down to the offspring. The third statement is essentially saying there is a competition between the species to which one is more able to survive in the given situations. These are the rules of life. Put them together with the ever changing environment and wait millions and billions of years and you have some absolutely amazing complexity. There was no central designer, it was all bottom-up. Even deniers of evolution accept these basic rules. They just deny that these rules can come together and by emergence construct the complexity of life that we see. Some deniers of evolution, even Kent Hovind, after enough talking, will admit there is truth in evolution. They just call it "micro-evolution". In fact, the complexity of life only suggests that there can be no central designer. For a central designer to put all of this life together, in the exact environments that they belong to, the amount of knowledge and work involved in such a project is enormous. It is just so incredibly unlikely that some central designer would have such skill and intelligence. Thus, it happens to be more plausible to argue for the complexity that we see in life not from central design but from bottom-up design, by complexity that emerges itself from basic rules of the components (individual organisms) follow.
Most everything that we see in the universe is the result of emergent complexity. The planets, stars, solar systems, galaxies, and so forth, none of this was centrally designed, it has emerged from the simple natural laws which govern the universe. The number of people living in a certain area, the way people walk, the shape of snowflakes, just about anything we can imagine is actually the result of bottom-up complexity. It was not mandated above from some person and it cannot be for the problem is just too complex, rather it all is the result of the emergence. Thus, it is more appropriate to ask the question, "what is centrally designed" or "what have we or can we design ourselves", because central design is an exception to complexity.