A Fractal model equipped with detail concept like that used in wavelet transforms is introduced and used to perform global and local deformations to objects. This fractal model based on Projected IFS attractors allows the definition of free form fractal shapes controlled by a set of points. The details concept taken from wavelet theory represents the geometric texture of the object. An approximation step is first done to fit the model to the object, this step is formulated as a non-linear fitting problem and resolved using a modified Levenberg-Marquardt minimization method. Global deformation can be achieved by moving control points or scaling and/or rotating the details extracted from the object. In the same manner local deformation can be applied with additional control points. In this work, we focus on 2D curves.