A central problem in computer vision is to detect, delineate (segment) and recognize objects in an image. One reason why this is difficult is that very little information specific to given types of objects is used during segmentation. Making use of information about an object's shape -- in particular, about how it grows -- should facilitate and improve the segmentation of that object. We introduce a 2D discrete growth model for shapes on a Cartesian grid, based on notions related to biological growth. By growth is meant an accretionary process occurring at the boundary of the shape. We introduce a new type of deterministic growth model based on the notion of time delay. Associating a delay with each direction defines a time delay kernel (TDK); such kernels produce classes of convex octagons, and sequences of TDKs can give rise to arbitrary convex polygons. We show that growth in a stochastic environment of facilitators and inhibitors, which decrease or increase the time delays respectively, is a plausible analog for biological growth processes. As an example, we present results which suggest that simple periodic growth processes in an environment describe the gross morphology of multiple sclerosis lesions at the scale afforded by magnetic resonance images.