Zebra rock is a strikingly patterned siltstone found exclusively in the East Kimberley region of northwestern Australia. Its features can include centimetre-scale stripes, spots, pillars and rods rich in hematite distributed throughout a bed of silica-rich clay, all of which can be exhibited even in the same basin of rock. The exact mechanism which forms these patterns is a subject of ongoing research. Of several proposals in previous studies, the two most prominent theories are redoximorphic banding in acid-sulfate soils, and Liesegang banding in an acidic hydrothermal system. In this report, we consider the former. A reaction-diffusion model is constructed consisting of the significant chemical reactions occurring in this system, which is catalysed by a population of acidophilic microbes. It may be shown that this model can exhibit Turing instability, and the resulting patterns that eventuate share a remarkable resemblance with the rock.