Fractals in Us

Human lungs: the lungs exhibit marvelous fractal branching, twenty levels of branching hidden within our chests.
Animal lungs: animal lungs also are fractal, but have geometries differing from that of human lungs. Note especially the manatee lung.
Arteries: the circulatory system also is fractal, to get (a small amount of) blood throughout the body.
Other examples: some nerve cells, the lining of the intestines, bone sutures, and others.
Fractal fluid injectors: the architecture of the lungs can be inverted to build a remarkably effective chemical mixer.
Heartbeat patterns: a chaotic heart is a healthy heart.