  Cellular Automata have been used since their introduction as a discrete tool
of modelization. In many of the physical processes one may modelize thus (such
as bootstrap percolation, forest fire or epidemic propagation models, life
without death, etc), each local change is irreversible. The class of freezing
Cellular Automata (FCA) captures this feature. In a freezing cellular automaton
the states are ordered and the cells can only decrease their state according to
this "freezing-order". We investigate the dynamics of such systems through the
questions of simulation and universality in this class: is there a Freezing
Cellular Automaton (FCA) that is able to simulate any Freezing Cellular
Automata, i.e. an intrinsically universal FCA? We show that the answer to that
question is sensitive to both the number of changes cells are allowed to make,
and geometric features of the space. In dimension 1, there is no universal FCA.
In dimension 2, if either the number of changes is at least 2, or the
neighborhood is Moore, then there are universal FCA. On the other hand, there
is no universal FCA with one change and Von Neumann neighborhood. We also show
that monotonicity of the local rule with respect to the freezing-order (a
common feature of bootstrap percolation) is also an obstacle to universality.
