  We present a solvable model of iterating cluster state protocols that lead to
entanglement production, between contiguous blocks, of 1 ebit per iteration.
This continues till the blocks are maximally entangled at which stage an
unravelling begins at the same rate till the blocks are unentangled. The model
is a variant of the transverse field Ising model and can be implemented with
CNOT and single qubit gates. The inter qubit entanglement as measured by the
concurrence is shown to be zero for periodic chain realizations while for open
boundaries there are very specific instances at which these can develop. Thus
we introduce a class of simply produced states with very large multipartite
entanglement content of potential use in measurement based quantum computing.
