We use the photosensitive chlorine dioxide-iodine-malonic acid reaction-diffusion system to study wavenumber locking of Turing patterns with spatial periodic forcing. Wavenumber-locked stripe patterns are the typical resonant structures that labyrinthine patterns exhibit in response to one-dimensional forcing by illumination when images of stripes are projected on a working medium. Our experimental results reveal that segmented oblique, hexagonal and rectangular patterns can also be obtained. However, these two-dimensional resonant structures only develop in a relatively narrow range of forcing parameters, where the unforced stripe pattern is in close proximity to the domain of hexagonal patterns. Numerical simulations based on a model that incorporates the forcing by illumination using an additive term reproduce well the experimental observations. These findings confirm that additive one-dimensional forcing can generate a two-dimensional resonant response. However, such a response is considerably less robust than the effect of multiplicative forcing.

External forcing can greatly affect the evolution of Turing patterns in reaction-diffusion (RD) media. Here, we employ spatially periodic illumination in a photosensitive RD system to create Turing structures that are repetitive in one direction. We then study their relaxation in the absence of light. These unforced, fishbonelike configurations undergo self-reorganization and establish stationary arrangements, some of which fully exhibit, while others partially or completely lose, the symmetry of the initially imposed pattern.