In plane geometry curves have a dimension of exactly 1 and no width. In nature, all curvilinear features have width, and most have dimension greater than 1, but less than 2. Many phenomena, such as coastlines, have the same "look," even when viewed at greatly varying scales. The former property is called "fractional dimensionality," and the latter is called "self similarity." Curves digitized from maps may be analyzed to obtain measures of these properties, and knowledge of them can be used to manipulate the shape of cartographic objects. An algorithm is described which enhances the detail of digitized curves by altering their dimensionality in parametrically controlled, self-similar fashion. Illustrations show boundaries processed by the algorithm.