This paper describes an interactive modeling method which allows a user to directly manipulate a fractal object defined by a recurrent iterated function system (RIFS). The method allows the user to nail points on the attractor to their current position, and drag other points to a desired position. The attractor changes shape to accomodate the new location of the dragged point. An incremental Newton’s method solves the system of equations generated to find a new set of RIFS parameters that satisfy the constraints. These solutions can be generated in real time for simple models on modern computer hardware, resulting in a fully interactive recurrent modeling system for designing models that closely match specific natural shapes.