A Scanning electron microscopic (SEM) study of a human lung cast revealed the bifurcation diagrams of the respiratory bronchiles with alveoli. Each respiratory bronchiole has about 30 alveoli. The number of the bifurcations of the tracheobronchial tree is estimated at 23th power of 2. The shape change patterns of alveoli during the respiration looked like the bifurcation diagrams leading to a chaotic attractor. Further, many bifurcated dendrites with a lot of synapses of Purkinje cells in cerebellar cortex may lead to a chaotic attractor.