There are two kinds of models, centralized or top-down, and distributed, or bottom-up models. Most physical models are of the first kind. They are governed by top-down laws that control entire systems. None of these suffices to describe even the simplest organism, which is complex and its properties emerge. Traditional mathematical tools fail to untangle life's complexity. We may distinguish between two kinds of complexity linear and non linear. Only the first can be resolved with traditional mathematical tools like logic, or induction. Life's complexity is non linear. Life is an oriented change.
Like a river that flows in one direction. Yet even a river could not serve as an adequate model for life, since its water is carried to the sea as such and does not change, while the ingredients of life continually transform. Fire might be regarded as best metaphor for life. It is born in the burning wood. As it raises upward, its color continually changes, from yellow to red, and blue. None of Artificial Life (AL) models can simulate a fire, neither a river, and yet some serious scientists claim that these simplistic models are a form of life, life in silico.
Cellular automata
S. Wolfram's book "A New Kind of Science" is an excellent introduction to cellular automata (CA). Yet it lacks two basic ingredients of life. His CA are infinite and immortal, while life is not. They consist of simple geometrical structures like triangles, while life is amorphous. Above all CA lack an essential ingredient of life, oriented turnover.(streaming). Why not augment CA so as to portray this property of life?
Click here to learn more
