We model phenomena intermediate between shape and texture by using space-filling applicative functions to modulate density. The model is essentially an extension of procedural solid texture synthesis, but evaluated throughout a volumetric region instead of only at surfaces. We have been able to obtain visually realistic representations of such shape+texture (hypertexture) phenomena as hair, fur, fire, glass, fluid flow and erosion effects. We show how this is done, first by describing a set of base level functions to provide basic texture and control capability, then by combining these to synthesize various phenomena. Hypertexture exists within an intermediate region between object and not-object. We introduce a notion of generalized boolean shape operators to combine shapes having such a region. Rendering is accomplished by ray marching from the eye point through the volume to accumulate opacity along each ray. We have implemented our hypertexture rendering algorithms on a traditional serial computer, a distributed network of computers and a coarse-grain MIMD computer. Extensions to the rendering technique incorporating refraction and reflection effects are discussed.