  A general mathematical method is presented for the systematic construction of
coupled map lattices (CMLs) out of deterministic cellular automata (CAs). The
entire CA rule space is addressed by means of a universal map for CAs that we
have recently derived and that is not dependent on any freely adjustable
parameters. The CMLs thus constructed are termed real-valued deterministic
cellular automata (RDCA) and encompass all deterministic CAs in rule space in
the asymptotic limit $\kappa \to 0$ of a continuous parameter $\kappa$. Thus,
RDCAs generalize CAs in such a way that they constitute CMLs when $\kappa$ is
finite and nonvanishing. In the limit $\kappa \to \infty$ all RDCAs are shown
to exhibit a global homogeneous fixed-point that attracts all initial
conditions. A new bifurcation is discovered for RDCAs and its location is
exactly determined from the linear stability analysis of the global quiescent
state. In this bifurcation, fuzziness gradually begins to intrude in a purely
deterministic CA-like dynamics. The mathematical method presented allows to get
insight in some highly nontrivial behavior found after the bifurcation.
