  The idea that the velocity of transmitting substance/energy trough space-time
is to be bounded is a fundamental concept in the science. To the most surprise,
it turns out that it is not always met. We demonstrate that the existing
approaches to the self-organization, another major concept in the science, let
the velocity of transmitting substance to be arbitrary. Further we prove that
only the boundedness of the velocity is not enough to ensure the
self-organization. That is why we develop radically novel approach to the
macroscopic evolution that not only reconciles the self-organization and the
velocity ansatz but in addition gives physically credible basis to phenomena
like Feigenbaum cascade and fluctuation-assisted bifurcations.
