The smallest program in architecture fits in one sentence: lay a brick, shift half a brick, repeat. Every course is a loop, and every brick is a row with a position, an angle and a check. This Friday’s ACTION sketch writes that table down. Once a wall is a list, a bond becomes a function and a building rule becomes a test.

The bond is not decoration

Why shift the brick at all? Eurocode 6 gives a plain answer. EN 1996-1-1:2005, clause 8.1.4.1, says units in an unreinforced masonry wall “shall be overlapped on alternate courses so that the wall acts as a single structural element.” For units up to 250 mm high, the overlap must be at least 0.4 times the unit height or 40 mm, whichever is greater. The clause writes down what generations of unnamed masons knew by hand. The shift is what turns a pile of clay into one element.

Take an NF brick, 240 × 115 × 71 mm (DIN 105). 0.4 × 71 is 28.4 mm, so the 40 mm floor applies. The sketch uses a 4.0 m × 2.40 m wall with 10 mm joints. In stretcher bond the worst overlap is 125 mm, and 0 of 462 checked bricks fail. In stack bond the overlap is 0 mm, and 448 of 448 bricks turn magenta, because the wall is really a row of separate columns. Drag the free-offset slider. At 10 % of the 250 mm module the overlap is 25 mm, and every brick fails. At 16 % it reaches 40 mm and the wall locks.

←TODAY: a 2026 wall can be exported as id, row, x, z, theta, one line per brick. →3012: Zurich’s walls are archived as derivations, and any apprentice can rebuild them from the rule. Fulcrum: the mason’s overlap and the robot’s freedom are the same variable.

Where the list became the design: the Strasbourg tower

PAZ Academy collaborated with KCAP on this project in Strasbourg, a brick tower 40 metres high. At that height a facade cannot be left to a hatch pattern chosen late. The bond, the joint width and every gap are values that someone decides and someone else must be able to check. That is the habit the sketch teaches: write the rule once, then run it over the whole elevation.

One honest note: the sketch is a teaching tool. The EN rule is written for unreinforced load-bearing masonry, and a real facade is checked against its own structural concept, so the sketch shows the rule as a reference, not a verdict on any real wall.

The price of turning a brick

PIXELS mode turns every brick of a stretcher wall about its own vertical axis, by an angle read from an image: grapes, a wave, or a word you type. The trade-off is plain: every degree of picture costs depth and bearing. Depth follows L·sinθ + T·cosθ. At 30°, a 240 mm brick needs 240·sin30° + 115·cos30° ≈ 220 mm of wall. The worst-supported brick rests on about 64 % of its footprint on the course below, and at 45° that drops to 44 %. These figures are a geometric teaching metric, not a structural verdict. Still, the overlap you give away for the image is the overlap the rule was protecting.

Atelier: An office drawing a brick facade in Archicad or Rhino often treats the bond as a hatch pattern, chosen late and checked by eye. As a list, the bond becomes a decision you can check, and a fabrication partner can read it directly. Monday move: export one elevation of your current brick project as a CSV of brick centres and run the 40 mm overlap test before the next coordination meeting.

Hack: Write the Eurocode overlap rule as one function and test your bond against it before you draw a single brick. The function covers both height bands of clause 8.1.4.1. The last line checks the sketch’s 16 % threshold for an NF unit.

const requiredOverlap = h => h <= 250 ? Math.max(0.4 * h, 40) : Math.max(0.2 * h, 100);
const module = 240 + 10;               // NF length + head joint, mm
const overlap = 0.16 * module;         // free offset at 16 % = 40 mm
console.log(overlap >= requiredOverlap(71)); // true; at 0.10 it is false

In Grasshopper + Rhino, the same logic fits in one C# script component. Since 2007, David Rutten’s canvas has let people learn a method while they build the project with it. The sketch’s core functions, layWall, headJoints, checkOverlap, rotateBricks and robotCSV, map to a handful of components. For the form-finding and optimisation layer on top, McNeel Europe’s Grasshopper Level 3 course with Ping-Hsiang Chen covered goals, forces and evolutionary search this spring.

Open the sketch. Break the wall with a stack bond, fix it at 16 %, turn it into grapes, then download the robot list. Start from the list, not the render.