Operations as Instructions

When a language model is connected to a modeller through the Model Context Protocol, it no longer describes a building: it builds one, call by call. McNeel’s RhinoMCP and the Blender Lab MCP server make this ordinary, and the question they leave open is an architectural one: what should the agent be allowed to call? A modeller’s own commands (box, move, boolean) give an agent the freedom to make any geometry and no reason to make any particular one. Every call is legal and none of them is a design move. This study tests the opposite assumption: that the tool set of an agentic CAD environment should be a vocabulary of architectural operations, so that every call is legible as a decision, every form can be rebuilt from its sequence of calls, and the limits of a method become something one can measure.

Peter Eisenman’s house studies are the historical case for this. Between House I and House X, design is written as operations on three kinds of element: a line, a plane and a volume are shifted, rotated, compressed and extended, and the house is the record of that sequence. It is the closest thing architecture has to an instruction set with a stated grammar, and it comes with its own test. In “Cardboard Architecture: House I”, the work must mark its regularities and at least part of their transformation. A method stated that precisely can be run by a machine, and it can be asked the question every instruction set must answer: what does it make, and when does it stop making architecture?

From a cube to a code

The study starts small. A cube, three elements and four operations give twelve cells: little enough to memorise, and the architecture lies in the order of application. Six houses made from one cube differ only in that order. A variant is stored as nothing more than its code, a string of the letters S, R, C and E (and, in my extension, D double, X split and V void), and the code rebuilds it exactly. This is the property an agent needs: the form is the trace of its instructions, so it can be read, repeated, varied and refused.

Left to run, a generator of this kind produces some eighty to a hundred forms a second, filed in eighty-one drawers. The number of forms never runs out. What runs out first is the record: run blind, a house loses the legible trace of its first operation within six to eight operations, use and reference within twelve to sixteen, and with numeric rules alone the house turns into a star of lines. A walker 2 m tall then asked a plainer question: in the first house no upper floor can be reached on foot. The rule that kept half the floor had protected canopy, not a house.

When the method runs out

To ask about exhaustion in Eisenman’s own terms, I counted the nine-square exactly. Three stacked nine-squares give 134,217,728 figures. Each was tested by an exact breadth-first search from the cube under his three moves (shear, compression, rotation) and against conditions read from “Cardboard Architecture: House I”: it stands, it marks the cube, it carries solid and void, a room inside, a centre or spine, a plane, a volume, a mirror one can conceive, and its last move can be named. Of all figures, 652,392 pass. They exist only from two to eight moves from the cube, peak at five, and none passes from nine on. The test that closes the window is the volume. A figure holds about 24 bits and a move costs more than six, so the record is full after four or five moves.

The answer I draw from this is that the method exhausts its reference, not its forms. For an agent this distinction matters more than any count: a tool set never runs dry of outputs, but it can run dry of outputs that are still about anything. No source I opened says Eisenman thought his method exhausted. That reading is mine.

Mid scale: 96 m

Scaling is a different question, and it is not additive. At a 128-cell block, one move changes less than one percent of the volume, so an operation has to become a law over parts. I first treated scale as a curriculum, carving a solid stage by stage from grid 3 to grid 128: each stage taught something (canyons at 6, a law over parts at 12, stairs and streets at 48), and the order of the stages mattered (a score of 0.74 against 0.71, 0.67 and 0.51 for other orders). The honest result was weaker than it looked: a fair random-box control scored as high, so the score could not see the figure. The two are shown side by side.

What held was the legible register at half scale: 64 cells, 96 m a side, white card with an ink line, single readable moves, and rooms named by form (nave, pit, cave, stair hall, slot, forest, pool, auditorium). Operations on the whole block, a twist or a funnel, read as gimmicks and were dropped. The next round gave every zone of the nine-square its own local system and let a second, offset division collide with the first: frontal slots crossed by an oblique band, cross voids with rooms in the quarters, a turned cluster against an orthogonal field, black poche against large light rooms. A strict walker on the finished voxels then corrected me: it reached only 5 percent of the floor, and an earlier figure of mine had been taken on a coarse grid before deforming. An access operation that cuts about 68 embedded stairs per block raised reach to 75 percent.

Large scale: 192 m and operations at scale

The last study stops carving. Elements are put in place, and an element recurs at three sizes: a line is a column, then a core; a plane is a wall, then a bar 7 to 14 m deep; a volume is a room, then a hall. The block is a nine-square of the cube filled with a census figure, and each built cell is a part of about 36 m that carries one of nine systems, each my reading of a house study at the size of the part: a Dom-ino frame, frontal planes, a cross after House VI, a volume in a moat after House III, an el after House X, a hall, a stair hall, a thickened mass with stairs in its poche, a court. Neighbouring parts never share a system. At 192 m about half the large parts become a nine-square again, and the rest stay whole as large rooms, their bays and rhythms grown with their size. An element that moves leaves its old place in lines: a turned part stands smaller inside its traced outline, and floors that step back leave the column grid of the full cube standing. This is how I read Eisenman’s condition that the work marks its transformation.

The anti-rules changed status along the way. In the urban-block study, a refusal did not scale: one offence anywhere refused a whole block, and by refusal alone no block passed all thirteen anti-rules at any size. Made into operations, they work. One part for each 72 m leaves the grid; one room must fail and is kept sealed, marked terracotta; a stair climbs into the air of a large room and stops; a column hangs from a ceiling; a tall room on the ground belongs to nobody; no floor is like the one below. For an agentic tool set this is perhaps the most transferable finding: a constraint that an agent can only obey or violate becomes, at scale, a call it has to make.

Benchmarks

All measures are taken on the finished voxels against a control with the same figures, cores and random streams, in which every part is a plain Dom-ino frame with no operation and no anti-rule. Means over 60 blocks at 96 m and 24 at 192 m:

The largest covered room is about 4,900 m² in a 96 m block and about 10,700 m² in a 192 m block. The operations buy formal difference and large rooms at a price in access, which the threaded stairs pay back to about 90 percent. Refusing the average raised the spread of the 60 mid blocks from 4.36 to 5.17, but that rise is built in, since removing the centre of a pool must widen it: it shows how much of the pool sat near the centre, not that what remains is better. One anti-rule was not met and was not made an operation: “no street you can see down” failed in 39 of 60 mid blocks and in every large one.

What this asks of agentic CAD

Read as research on MCP-CAD, the five studies point to four requirements. The tools should be operations on elements, not commands on geometry, so that a model is the record of its calls. The order of calls is part of the design, and a tool set should keep it as data. Constraints at scale must be operations the agent performs, not filters that refuse its results. And every generator needs a measure and a control beside it: the census, the walker and the plain Dom-ino frame did more to correct my claims than any rendering, and twice they showed that an earlier figure of mine was wrong.

These studies were made as code in agent sessions, and the drawings come from voxel volumes and the lab’s own path tracer, not from a commercial modeller. The next step is to expose the same operations as the tools of an MCP server inside Rhino and Blender, so that an agent models with shift, rotate, compress and extend rather than with boxes, and so that its taste, measured over its logged calls, becomes a subject of design review.

Every threshold, weight and percentage is my choice, and the nine systems are my readings of house studies, not reconstructions. House III’s rotation and House X’s quadrants are read from secondary accounts; the hanging column of House VI is sourced only through secondary reports. The measures are proxies: “within 9 m of a support” is not a structure, and plan depth is not daylight. Nothing here is a claim about how Eisenman worked.