Gold-black coatings formed by evaporation and subsequent sublimation of pure gold in an inert low-pressure atmosphere are used to enhance absorption of thermal radiation. Previous attempts to predict the spectral absorptivity of gold-black coatings have typically assumed a granular continuum with effective bulk optical properties. In the current effort the principles of diffusion-limited aggregation (DLA) are applied to mimic the observed microstructure of actual gold-black layers consisting of a random fractal distribution of dendritic gold filaments that are postulated to behave as dipole antennas. Absorption of incident electromagnetic radiation by individual filaments is predicted using a unique time-dependent lossy antenna model drawing on the Drude-Sommerfeld free-electron theory. Single-filament spectral absorptivities are combined based on the DLA microstructure model to predict the spectral and, for the first time, the directional absorptivity of the gold-black layer. Results for normal spectral absorptivity are shown to be in good agreement with measurements reported in the literature.