  Localised patterns are often observed in models for dryland vegetation, both
as peaks of vegetation in a desert state and as gaps within a vegetated state,
known as `fairy circles'. Recent results from radial spatial dynamics show that
approximations of localised patterns with dihedral symmetry emerge from a
Turing instability in general reaction--diffusion systems, which we apply to
several vegetation models. We present a systematic guide for finding such
patterns in a given reaction--diffusion model, during which we obtain four key
quantities that allow us to predict the qualitative properties of our solutions
with minimal analysis. We consider four well-established vegetation models and
compute their key predictive quantities, observing that models which possess
similar values exhibit qualitatively similar localised patterns; we then
complement our results with numerical simulations of various localised states
in each model. Here, localised vegetation patches emerge generically from
Turing instabilities and act as transient states between uniform and patterned
environments, displaying complex dynamics as they evolve over time.
