Current fractal tools lack the level of control necessary to model specific natural structures. For example, many fractal models of trees have been constructed, but given a particular tree, it would be difficult to represent the tree's specific shape using current models of fractal modeling. The recurrent modeling project identifies three aspects to this problem, and attempts to solve each with several new fractal modeling tools. Objective I: Recurrent Model Representation. Recurrent modeling strives to elevate fractal representation to the level of sophistication that smooth surfaces enjoy in computer-aided geometric design by translating their classical self-referential representation into standard implicit and parametric forms. Recurrent modeling also attempts "procedural geometric instancing," and enhancement of the classic object instancing paradigm that enables it to more efficiently represent the development fractal models currently specified by L-systems. Objective II: Interactive Recurrent Modeling. Recurrent modeling extends the tools of computer-aided geometric design to fractal geometry. A direct manipulation interface provides real time feedback in the fractal modeling process. The implicit formulation from the previous objective allows the application of standard blending formulations specifically designed for natural modeling. Extending constructive solid geometry to include fractal models supports the construction of complex shapes from primitives. Objective III: Automatic Recurrent Modeling. Recurrent modeling attacks the inverse problem of fractal geometry: "find the parameters of a fractal model that approximates a given shape" from the domain of model-based computer vision. The second PI is an NSF-supported model-based computer vision researcher. His unique perspective on this problem resulted in a new solution, called "similarity hashing". Similarity hashing successfully detects self-similarity and returns the paramete rs of the selfsimilar model in initial tests. Recurrent modeling continues this research to develop an automated system for discovering selfaffinity in natural structures. The new tools recurrent modeling proposes would impact the fields of computer graphics and forest science. The new tools would represent highly detailed geometrics, such as a forest and crops. Such models would have applications in image synthesis, particularly in animation, virtual environments, physically- based modeling and remote sensing. As the smooth representations of computer-aided geometric design aid manufacturers, the efficient representations of detail proposed by recurrent modeling representations would aid the study of the environment. ***
