This document discusses the design and simulation of a self-affine rectangular fractal antenna with electromagnetic bandgap (EBG) structures. The antenna is designed on a substrate with a dielectric constant of 4.4 and thickness of 1.6mm. The basic rectangular patch antenna is modified through two iterations of fractal geometry to produce a multiband antenna. EBG structures are added surrounding the antenna. Simulation results show the antenna resonating at multiple frequencies with increased iteration, providing bandwidth enhancement and size reduction compared to the basic patch antenna. Good agreement is achieved between simulated and experimentally measured results.