Experimental PSN632408 manipulations show that auxin influences the site on the cell membrane where patches of ROP form, and hence the site on the cell of root hair outgrowth. Moreover, in a mutant background in which auxin transport is severely disrupted exogenous auxin induces root hairs to grow at the end of the cell nearest to the auxin source, even when this is the opposite end from normal. Molecular mechanisms of root hair positioning have eluded conventional genetic approaches. It has proved difficult to isolate mutants in which the subcellular location of root hair outgrowth is altered, and difficult to interpret those mutants that do exist, including rhd6, procuste1, and auxin and ethylene mutants development in limbs. More recently, theoreticians have started to apply the same types of ideas at the level of a single cell. Recent studies suggest that related Rho GTPases from other organisms are well suited to spontaneous pattern formation via a Turing or Turing-like mechanism. Turing patterns are sometimes referred to as diffusion-driven instabilities because a key condition is that the different chemicals diffuse at different rates. In the ROP system the active form of type I ROP is expected to have a lower diffusion coefficient than the inactive form on account of it being tightly associated with the cell membrane via an S-acyl group, and so ROPs, like Rhos, are naturally suited to act as Turing morphogens. Existing studies of pattern formation by Rhos have focussed predominantly on explaining cell polarity. In contrast, the pattern we seek to explain in RH cells is more complex, in that the hair is usually set a little way back from the cell end, and that there exist various mutant phenotypes with multiple hairs. A basic Turing mechanism by Songorine itself is not enough to give the patterning of ROP localisation seen in root hair cells. In this paper we hypothesise that the extra factor required is a gradient in either the parameter controlling autocatalysis of ROP activation, or in the rate of production of inactive ROP. The ability of a regulatory gradient to stabilise Turing patterns has been noted before, although this important property is rarely mentioned and has been little studied.