We simulate tracer transport in a two‐dimensional porous medium. We provide justification for the use of a fractal scaling law to characterize the spatial variability of rock properties, leading to a fractal rock property model. A methodology based on the fractal model discussed is applied to experimental data to generate a “fractal porous medium” and to solve the associated flow and tracer transport problems. Tracer breakthrough curves are computed for three different breakthrough distances. An advection‐dispersion matrix diffusion model, a channeling model, and a channel‐network model are used to assess objectively the relative contributions of Fickian dispersal processes and channeling within simulated tracer transport through the fractal medium. The results reveal early breakthrough is fast‐channel dominated, while later breakthrough is predominately Fickian.