Many natural sounds, such as those arising from rain, fire, or a swamp full of insects, are produced by a concurrence of many similar acoustic events that overlap in time. We refer to these sounds as "auditory textures". if a set of statistics underlie texture perception, one should be able to synthesize textures that sound like real-world textures by generating signals that match their statistics. We designed a texture synthesis algorithm to test this idea. Although matching statistics of individual auditory filters (replicating the power spectrum of the original signal, among other things) is inadequate to produce compelling synthesis, statistics of intermediate complexity, capturing simple dependencies between filters, can produce compelling synthetic examples of many natural sound textures.