I describe a process for creating dendritic fractal tiles that admit monohedral two-color tilings. At each iteration of the construction small untiled spaces are present. These decrease in density with each iteration, disappearing in the fractal limit. I present dendritic fractal tiles based on regular square and hexagonal tilings. Some of these tiles are closely related to well-known fractal curves. The website (link below) contains similar content to the paper but includes some animations and a few additional curves.