Information Technology Reference
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15.7 Chaos Theories
From the perspective of the system, life behavior can be defined as the non-linear,
non-equilibrium open system in physics at first. So, the special behavior of this
kind of systems is natural oscillation, i.e., limited period and chaos. The
particular behavior of life is concerned by ontologism and advanced information
processing. In artificial life, its formation principles are most important. The
limited periods can be divided into stable ones and unstable ones. The natural
oscillation is called the stable limited period. Limited oscillation and chaos are
the two respects of structure stability. The only thing can distinguish between
them is that the difference of initial conditions of limited period greatly
influences the future movements. In chaos, the difference of the initial conditions
is expanded with time quickly, so it is difficult to reproduce it approximately.
This kind of property is called orbit instability, which forms obvious contrast to
the ordering of the orbit stability based on limited period. The dynamics of the
nature can be divided into order and chaos. The regular behavior of order is the
periodic solution. Other chaos systems are complex, with unpredictable behavior
in the long term. From the perspective of time development, both of them are
basically the dynamics systems. Therefore, life bodies are the compositions of
chaos and order.
What is it about the computation capabilities of order and chaos, which are
taken as the formation principles of characteristic phenomena emerging from life
behavior? At first, ordered systems have the periodic complexity, so it is
impossible to implement the highly complicated computation. There are strict
rules in the chaos systems. Because of this, it is difficult to compute the unstable
behavior of their orbits theoretically. Thus, we only consider the life behavior
seen at the edge of chaos. In this way, the basic operations of information, such
as storage, transmission, transformation, etc, can be implemented in the mixed
systems of order and chaos:
(1) The information storage is obtained from stable period dynamics of ordered
systems.
(2) The transmission and transformation of information can be realized using
unstable dynamics of chaos systems.
Langton found that people could make the one-dimensional cellular
automaton continuously change its state as “fixed-value type → periodic type →
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