Gaudi's works are always called "organic," and "flowing" is often used (appropriately) to describe their fluid shapes.  But apart from some Art Nouveau influence, his original model seems biological, particularly botanical.  Roots, leaves, and petals seem to have been sources.  And funghi seem to have been influential, too.   A viewer studying the ceiling of a Gaudi structure, especially the Sagrada Familia, has the sense of looking up at the ceiling of a cavern, and of examining the roots of plants from below.  And the ceiling in the pavilion at Park Guell seems partly inspired by mushrooms.

Below: Sagrada Familia

Below: Park Guell

A mushroom-inspired ceiling at Park Guell?

Above: Casa Batllo facade looking up

Below: On the roof of Casa Batllo.

Below: Park Guell scenes

That isn't to say Gaudi ignored animals.  His salamander (known as "el drac," the dragon) trades a mosaic of ceramic fragments for a skin of living scales.

Finally, it seems to me Gaudi did not engage in purposeless whimsey, except when his obvious purpose was to entertain, as in Park Guell in Barcelona.  His controlled exuberance injected, however briefly, some humanity into architecture.  He liberated structures from impersonal and rigid formalism, but his vision was not ultimately influential to modern architecture.  Nonetheless, his work remains a thought-provoking and iconoclastic model that is far more entertaining than most modern structures. And it may yet come into vogue, especially if Richard Branson can make Virgin Galactic successful.