Why did Kamakura-period hill gardens become associated with Mount Fuji?

During the Kamakura period (1192–1333), Japanese garden design shifted from imitation toward greater creativity and the use of symbolism. Hill gardens, known as tsuki-yama, became associated with Mount Fuji because it was regarded as the mountain of "ideal form".1

Because these gardens were constructed on a small scale—often using a mound of earth only about 30 feet high to represent a mountain—the primary intention was to capture the spirit and essence of the landscape rather than to replicate its physical features exactly. Consequently, the association with Mount Fuji served as a symbolic framework, allowing designers to evoke the grandeur of an ideal landscape within the confined space of a garden through the use of carefully placed hills and ponds.1