Ibiza, the third largest of the Balearics, began to grow from a quiet, little-known island into a playground for the rich and an enclave for artists in the 1950s and 1960s. The island's brilliant, whitewashed houses reflect not only the summer sun, but 300 years of Moorish rule, earning it the nickname of 'Isla Blanca' or White Island. The town of Ibiza, also known as Eivissa, is a delightful comb…