  We investigate the damage spreading effect in the Fortuin-Kasteleyn random
cluster model for 2- and 3-dimensional grids with periodic boundary. For 2D the
damage function has a global maximum at $p=\sqrt{q}/(1+\sqrt{q})$ for all $q>0$
and also local maxima at $p=1/2$ and $p=q/(1+q)$ for $q\lesssim 0.75$. For 3D
we observe a local maximum at $p=q/(1+q)$ for $q\lesssim 0.46$ and a global
maximum at $p=1/2$ for $q\lesssim 4.5$. The chaotic phase of the model's
$(p,q)$-parameter space is where the coupling time is of exponential order and
we locate points on its boundary. For 3-dimensional grids the lower bound of
this phase may be equal to the corresponding critical point of the $q$-state
Potts model for $q\ge 3$.
