  We construct random dynamics on collections of non-intersecting planar
contours, leaving invariant the distributions of length- and area-interacting
polygonal Markov fields with V-shaped nodes. The first of these dynamics is
based on the dynamic construction of consistent polygonal fields, as presented
in the original articles by Arak (1982) and Arak and Surgailis (1989, 1991),
and it provides an easy-to-implement Metropolis-type simulation algorithm. The
second dynamics leads to a graphical construction in the spirit of Fernandez,
Ferrari and Garcia (1998,2002) and it yields a perfect simulation scheme in a
finite window from the infinite-volume limit. This algorithm seems difficult to
implement, yet its value lies in that it allows for theoretical analysis of
thermodynamic limit behaviour of length-interacting polygonal fields. The
results thus obtained include the uniqueness and exponential $\alpha$-mixing of
the thermodynamic limit of such fields in the low temperature region, in the
class of infinite-volume Gibbs measures without infinite contours. Outside this
class we conjecture the existence of an infinite number of extreme phases
breaking both the translational and rotational symmetries
