Creating surfaces with intricate small-scale features (microgeometry) and detail is an important task in geometric modeling and computer graphics. We present a model processing method capable of producing a wide variety of complex surface features based on displacement mapping and stochastic geometry. The latter is a branch of mathematics that analyzes and characterizes the statistical properties of spatial structures. The technique has been incorporated into an interactive modeling environment that supports the design of stochastic microgeometries. Additionally a tool has been developed that provides random exploration of the technique's entire parameter space by generating sample microgeometry over a broad range of values. We demonstrate the effectiveness of our technique by creating diverse, complex surface structures for a variety of geometric models, e.g. arrowheads, candy bars, busts, planets and coral.