Goose down has superior thermal insulating properties as a filler material used widely as an insulator in textile products. Its particular “tree” structure is expected to attribute greatly to this insulating property. In this paper, fractal structures of the down “tree” are observed using scanning electron microscopy (SEM), and the configuration characteristics of goose down are described quantitatively by local fractal dimensions. From two expects, the local fractal dimensions were calculated both theoretically and experimentally, revealing its value to be very close to the golden mean, 1.618. This near-optimal fractal dimension may be attributable to the excellent thermal insulation of goose down assembly, and the potential applications of such a fractal structure are also discussed.