  A new angle of view is proposed to find the simple rules dominating complex
systems and regular patterns behind random phenomena such as cities. Hierarchy
of cities reflects the ubiquitous structure frequently observed in the natural
world and social institutions. Where there is a hierarchy with cascade
structure, there is a rank-size distribution following Zipf's law, and vice
versa. The hierarchical structure can be described with a set of exponential
functions that are identical in form to Horton-Strahler's laws on rivers and
Gutenberg-Richter's laws on earthquake energy. From the exponential models, we
can derive four power laws such as Zipf's law indicative of fractals and
scaling symmetry. Research on the hierarchy is revealing for us to understand
how complex systems are self-organized. A card-shuffling model is built to
interpret the relation between Zipf's law and hierarchy of cities. This model
can be expanded to explain the general empirical power-law distributions across
the individual physical and social sciences, which are hard to be comprehended
within the specific scientific domains.
