Polymer behavior in external fields is modeled using fractal Brownian motion. The chain dimensions of polymer chains with and without excluded volume show a contour length dependence of N-v where v = h - 1. Chains with excluded volume have h = 3/5, chains without excluded volume, Gaussian chains have h = 1/2, and for chains in the collapsed state h = 1/3. This nonphysical result points to the distinction between fractals as models of the trajectory or path of a polymer that are self-similar on all length scales and real polymers that possess a lower and upper limit for self-similarity.