  We present simulations of causal dynamical collapse models of field theories
on a 1+1 null lattice. We use our simulations to compare and contrast two
possible interpretations of the models, one in which the field values are real
and the other in which the state vector is real. We suggest that a procedure of
coarse graining and renormalising the fundamental field can overcome its
noisiness and argue that this coarse grained renormalised field will show
interesting structure if the state vector does on the coarse grained scale.
