Once in, I want to move in—aspirationally and kinetically. The hall streams. The stairs surge. There are no edges, no corners. Walls glide into ceilings. Rooms flow into rooms. It is a peristalsis house. But light, cheer, air, and comfortable proportions are everyplace. The design is meant fully for people and, what with all the tourists, is full of them. They are in good spirits, as the spirit of the house demands. Every detail is crafted to delight. Even the air shaft is a masterpiece, tiled in shades of azure, deep-tinted at the top and gradually lightening to spread sun evenly to all floors.

Three blocks up Passeig de Gràcia, Casa Milà, completed in 1910, is better yet. The big apartment building has the hard but fluid segmented continuity of an invertebrate, though its limestone shell is really supported on the kind of steel skeleton introduced not long before by Chicago architect William Le Baron Jenney. Casa Milà insinuates itself into its corner lot with a lovely dead-bleached-insect grace. Some 150 windows, all seemingly different, are arranged in sinuous asymmetry. Some are armed at their sills with ferocious railings of wrought iron that, to me, seem abstractions of mandibles, tentacles, stingers, and jellyfish sacs. The roof is separately aggressive, a banked and mounded parapet with dormer windows that could serve as embrasures, and chimneys molded to evoke Catalan knights in armor.

Casa Milà is a carapace, a fortress, but a fortress of domestic pleasantry. The apartments wander through the complexity of the building’s form, so their floor plans look insane. But Gaudí didn’t like blueprints or even renderings. He preferred to work from models. And the apartments are models of open-plan living, lofts in advance of fashion, except with better natural light, greater ventilation, more common sense, and a happier mood. Few lofts today have a sewing room, and none have ceiling plaster whipped like meringue.

All of Gaudí’s works, however outwardly unruly, proceed from internal discipline. His father was a boiler-maker. Gaudí loved geometry. To determine the catenary curves of arches, he would tack a sketch of a foundation plan on the ceiling, hang loops of string, and attach weights along the loops in proportion to down forces. Then he’d take a photograph, turn the print upside-down, and get his elevation view. Gaudí pioneered the parabolic arch, with its perfect distribution of load. The arches beneath Casa Milà’s stone roof are so strong, each is built with a single course of upended bricks.

Gaudí also had a sense of proportion. Every design is sized to the effect intended. Casa Milà, for example, should be scary. But it’s too human in scope and scale. It’s charming instead, like a child’s drawing of something scary—if your child were Degas.

Less than a mile northeast of Casa Milà is La Sagrada Família (Holy Family) basilica, where Gaudí was operating on a scale that’s superhuman. He began work on the church in 1883, when he was 31. From 1914 until his death in 1926, he devoted himself solely to the project, which is still under construction and maybe always will be.