Integrating an absorbing thin film into a resonant cavity is the most practical way to achieve perfect absorption of light at a selected wavelength in the mid-to-far infrared, as required to target blackbody radiation or molecular fingerprints. The cavity is designed to resonate and enable perfect absorption in the film at the chosen wavelength . However, in current state-ofthe-art designs, a still large absorbing film thickness ( /50) is needed and tuning the perfect absorption wavelength over a broad range requires changing the cavity materials. Here, we introduce a new resonant cavity concept to achieve perfect absorption of infrared light in much thinner and thus really nanoscale films, with a broad wavelength tunability using a single set of cavity materials. It requires a nanofilm with giant refractive index and small extinction coefficient (found in emerging semi-metals, semi-conductors and topological insulators) backed by a transparent spacer and a metal mirror. The nanofilm acts both as absorber and multiple reflector for the internal cavity waves, which after escaping follow a fractal phasor trajectory. This enables a totally destructive optical interference for a nanofilm thickness more than 2 orders of magnitude smaller than . With this remarkable effect, we demonstrate angle-insensitive perfect absorption in sub -/100 bismuth nanofilms, at a wavelength tunable from 3 to 20 m.