Antoni Gaudí's Sagrada Família represents an architectural method in which form is not drawn by an architect but 'found' by gravity. Gaudí regarded the flying buttresses of the Gothic cathedral — the crutches a building adds outside to stay in balance — as a flaw, and wanted to be rid of them. His solution was physical.

Gaudí hung chains and small weight-bags on strings from a ceiling; each chain naturally takes a catenary (chain-curve) form under its own weight. This curve carries only tension; inverted, it gives a perfect arch or column carrying only compression. Gaudí photographed this hanging model and turned it upside down, thereby obtaining the geometry of leaning columns and arches that produce no lateral thrust and therefore need no buttress. The structure stands because it imitates the natural flow of forces — the form is the solution found by material and weight, not by drawing.

The towers and vaults are defined by 'ruled surface' geometries such as hyperboloids and helicoids: though they look curved, because they are generated by rotating straight lines they are easy to cut in stone and to calculate. Gaudí thus builds a language that looks organic but is wholly mathematical and structural. Begun in 1882 and still under construction, the work is today also the subject of contemporary engineering that resolves Gaudí's models with digital parametric tools. Sagrada Família is one of the rare buildings in which structure and form cease to be two separate things and become one.