Behavior of various complexity functions

For a nonempty closed set Ω⊂AN with 2≤#A<∞, we consider 3 complexity functions of k=0,1,2,…: (1)(block complexity) ,(2)(maximal pattern complexity) ,(3)(minimal pattern complexity) , where # denotes the number of elements in a set, and Ω|S is the restriction of Ω to S⊂N. If holds, then the above 3 complexities coincide and are called uniform complexity, denoted by pΩ(k).Behaviors of these 4 complexity functions are discussed.