A cord can only pull. Whatever shape a hanging cord settles into, it holds that shape by tension alone, with no bending. Turn the shape upside down and every pull becomes a push, so the same curve now stands in pure compression. Three generations of builders carried that one idea from a single chain to a whole roof. This week you can watch the cord find its shape in a browser sketch.

The sketch

The ACTION sketch hangs a net of 14 × 14 nodes. Springs run along the grid, with one diagonal per cell. The four corners are pinned at height 0 and two more supports are lifted. Verlet relaxation then lets gravity settle the net. Edges shade from cyan (slack) to magenta (load path), and supports show in lime. A faint ghost at about 8.5 % opacity is the same net mirrored in height: the compression form.

• Tag dropdown. Eight options: gaudi (the default), frei-otto, catenary, vault, eth-brg, gridshell, membrane, parametric. The tag only seeds which two edge-midpoint supports are lifted, and by how much (1.4 to 4.0 grid units). The physics is the same for every tag.
• reseed. Same tag plus a time stamp, which gives you a new pair of lifted supports and a fresh drape.
• view / remix the code. Shows the running JavaScript and a three-step learn-it list.
• download sketch. Saves the self-contained HTML file so you can remix it.
• Readout. seed("tag") -> 0x… shows the hash of the tag.

You cannot drag nodes, change gravity or move supports with the mouse. There are no sliders and no real units. The sketch shows how the method behaves. It is not a structural calculation.

←TODAY: in 2026 you can hang a net in a browser tab and re-hang it with one click. →3012: the shells that last are the ones anyone can derive again from gravity and a set of supports. Fulcrum: the method outlasts every tool that runs it, from lead sacks to RhinoVAULT.

Three generations, one rule

Antoni Gaudí built the hanging model for the Colònia Güell church at 1:10. Hemp ropes carried the lines of force, lead-filled sacks stood in for the loads, and canvas sheets traced the vaults and walls. According to Wikipedia’s entry on the church, he photographed the model, flipped the image and drew over it. All that survives of the model is one image in a book by Josep Francesc Ràfols i Fontanals. The crypt, built from 1908 to 1915, is part of UNESCO’s “Works of Antoni Gaudí” World Heritage listing, first inscribed in 1984.

Frei Otto scaled the method up to a whole hall. For the Multihalle Mannheim, built for the 1975 Bundesgartenschau, he used Hängemodelle: nets and chains hung freely, so only tension acts in them. As ingenieur.de reported on 04.06.2026, the hall covers about 7,400 m² with no interior supports and spans up to 85 m. It is built from about 72 km of 5 × 5 cm timber laths laid on a 50 cm grid.

Philippe Block turned the method into mathematics a computer can solve. His 2009 MIT PhD set out Thrust Network Analysis (TNA), which his Wikipedia page describes as a method for assessing historic unreinforced masonry vaults and for designing compression-only shells. A form diagram and its reciprocal force diagram do the work of Gaudí’s sacks. At ETH Zürich, his Block Research Group, working with Tom Van Mele and others, built TNA into the RhinoVAULT plugin and the open-source COMPAS framework. At the 2016 Venice Biennale, the Armadillo Vault spanned 16 m with 399 limestone stones and no mortar, and it was 5 cm thick at its thinnest point. Designing Buildings credits Block and Van Mele with Ochsendorf, DeJong & Block and The Escobedo Group. The vault was assembled first in Texas, then rebuilt in Venice by master stonemasons in just over two weeks. Their names belong in this story as much as the method does. Closer to home, the group’s 2011 brick vault prototype at Wolfgang-Pauli-Strasse 15 in Zürich went up in six weeks from two layers of flat clay bricks. Baunetzwissen credits Matthias Rippmann, Lara Davis and Block as architects, with structure by Davis and Tom Pawlofsky.

The trade-off is this: a funicular shape is only optimal for the load case it was hung with. If the loads change, the thrust line leaves the shape.

Atelier: A Zürich office running Rhino and Grasshopper can now generate a vault in seconds. The question in a design review is no longer what the vault looks like but which loads it was hung with. Monday move: make it office policy that every form-found surface ships with a short note listing its supports, its load case and its solver.

Hack: Hang a chain in four lines of Python, then flip it into an arch. On each pass, every free node moves to the midpoint of its two neighbours and is pushed down by a constant load. Inverting the settled chain gives the thrust line. Because the load per node is constant along x, this converges to a parabola. Weight the load by segment length and you get a true catenary.

import numpy as np; y = np.zeros(15)          # 15 nodes, ends pinned at 0
for _ in range(5000):
    y[1:-1] = 0.5*(y[:-2] + y[2:]) - 0.01     # neighbours pull, load pushes down
print((-y).round(2))                          # flip: tension becomes compression

Open the sketch, reseed it five times on the gaudi tag, and watch the magenta load path move each time the supports move.