The Bray–Liebhafsky reaction is one of many intricate chemical systems that is known to exhibit periodic behaviour. Although the underlying chemistry is somewhat complicated and involves at least ten chemical species, in a recent work we suggested a reduced two-component model of the reaction involving the concentrations of iodine and iodous acid. Although it is drastically simplified, this reduced system retains enough structure so as to exhibit many of the oscillatory characteristics seen in experimental analyses. Here, we consider the possibility of spatial patterning in a nonuniformly mixed solution. Since many practical demonstrations of chemical oscillations are undertaken using circular containers such as beakers or Petri dishes, we develop both linearized and nonlinear pattern solutions in terms of cylindrical coordinates. These results are complemented by an analysis of the patterning that might be possible within a rectangular domain. The simulations give compelling evidence that spatial patterning may well be feasible in the Bray–Liebhafsky process.
