Formation and maintenance of complex systems

A complex system is often identified by the absence of a characteristic length, e.g. as in a fractal. A very large system subject to a fragmentation and/or aggregation dynamics passes through such complex configurations. We study statistically creation and maintenance of such configurations in space dimensions d = 1 to 5 and find that they are easily created (maintained) for small (large) d. An intermediate d such as d = 3 seems to be ideal for the creation and maintenance of complex systems. This has consequences in a statistical description of the universe.