Fractal tilings based on kite- and dart-shaped prototiles

Abstract A family of “fractal tilings”, or “f-tilings” is presented in which the curves defined by the boundaries are fractals. There are two distinct branches, one with three f-tilings based on kite-shaped prototiles, and the other with three f-tilings based on dart-shaped prototiles. This appears to be the first report of a systematic exploration of tiling-like constructs with fractal character.