  We present bulk tensor networks that exactly represent the ground states of a
continuous family of one-dimensional frustration-free Hamiltonians. These
states, which are known as area-deformed Motzkin and Fredkin states, exhibit a
novel quantum phase transition. By tuning a single parameter, they go from a
phase obeying an area law to a highly entangled rainbow phase, where the
half-chain entropy scales with the volume. Using the representation of these
ground states as superpositions of random walks, we introduce tensor networks
for these ground states where local and global rules of the walker are baked
into bulk tensors, thereby providing an efficient description of the ground
states (some of which satisfy a volume law scaling of entanglement entropy).
