  The unreduced, universally nonperturbative analysis of arbitrary interaction
process, described by a quite general equation, provides the truly complete,
"dynamically multivalued" general solution that leads to dynamically derived,
universal definitions of randomness, probability, chaoticity, complexity,
fractality, self-organisation, and other properties, extending their axiomatic
introduction in the conventional, dynamically single-valued (unitary) theory
(physics/9806002, physics/0211071). Any real system emergence, structure, and
behaviour can be expressed now by the universal law of conservation, or
symmetry, of complexity that unifies extended versions of any (correct)
symmetry, law, or "principle". Both the observed world structure and its
unreduced dynamics result from that universal, unique symmetry, instead of
formal imposition of separated, broken and simplified symmetries upon the
existing, postulated structures in the unitary world "model". Whereas any
unitary "symmetry" is regular and therefore practically always "spontaneously
broken" (violated) in the real world dynamics, the universal symmetry of
complexity remains always exact, but unites different, irregular, dynamically
nonlinear, and intrinsically unstable patterns of unreduced world structure. It
also provides the rigorous, dynamically derived expression of the ``arrow of
time" (generalised entropy growth law) applicable to any real, necessarily
complex system, from elementary particle to the universe. Particular
applications of the universal symmetry of complexity, from fundamental physics
to biology and theory of consciousness, provide old mysteries solutions and new
research perspectives.
