We have constructed a spatiotemporal nonlinear system model based on induced reflection gratings to study the energy exchange that results in pattern formation inside a photorefractive crystal. Along with a phenomenological model to illustrate the buildup of the reflection gratings caused by counterpropagating waves inside the photorefractive material, we have used a wave equation to simulate the spatiotemporal evolution of scattered light into hexagonal and ring patterns in a photorefractive material. Conditions conducive to hexagonal and ring formations are found, and the stability of the eigenmodes are investigated.