Complex (Self-Organizing) Systems

"A complex system is one whose component parts interact with sufficient intricacy that they cannot be predicted by standard linear equations; so many variables are at work in the system that its overall behavior can only be understood as an emergent consequence of the holistic sum of all the myriad behaviors embedded within. ... the whole is more than the sum of its parts."
(Artificial Life by Steven Levy, 1993, p.8.)

Class I: Class one cellular automata are based on simple rules. They have the tendency to die out after a few generations.

Class II: Class two cellular automata are based on periodic rules. They start out randomly but quickly become periodic. This can be seen in their repeating pattern.

Class III: Class three cellular automata are based on random rules. They have the distinct appearance of having basically junk on the screen with no definable shapes.

Class IV: Class four cellular automata are based on complex rules. Complex because no one really knows the criteria for it to be considered a complex rule.

Class I	Class III	Class IV

• Non-Linear systems under stress may be deterministic, but they are not predictable.
  非力学システムは、確定的だが予想不可能である。
  
  
• Biological models supplement mechanical models.
  生物学的モデルは力学モデルを補足する。
  
  
• Living systems balance between chaos and order.
  生命システムはカオスと秩序の間でバランスを保っている。
  
  
• Creativity and self-organization are possible even in deterministic systems.
  創造性と自己組織化は、確定的システムの中でも可能である。