The polyacrylamide-methylene blue-oxygen system reveals a variety of complex concentration patterns. Chevron and white-eye patterns develop from simple hexagons in a slow, continuous transition process. A third type of structure (honeycombs) forms from either white-eye patterns or hexagons. This transition occurs rapidly along propagating fronts. Two-dimensional Fourier analyses reveal that the complex patterns have a simple structure and that the wave vectors of the initial hexagons an conserved in all transitions, Quantitative data on surface undulations of the gel are presented. The surface structure resembles the structure of the observed methylene blue patterns. A schematic phase diagram is presented that characterizes the pattern geometry in terms of reaction time and initial sulfide concentration.