Tiling & Patterns

Attractors and fields give you variation; tiling gives you the units that variation acts on. Before a facade can have openings that grow toward a corner, it needs to be divided into a coherent set of cells - and how you divide it is a real design decision with consequences for looks, fabrication and structure. A parametric pattern system is a rule for partitioning a surface into repeatable, editable pieces, and it is one of the most practical skills in the whole course.

The simplest is the grid: divide a surface in U and V (Divide Surface, or Isotrim / Surface Split) into a tidy array of quads. Grids are easy, planar and cheap, and most buildings are gridded for good reason. But grids can read as monotonous, and on a doubly-curved surface their quads stop being flat - a fabrication headache we will return to.

Beyond the grid lies a family of richer tilings - Voronoi, triangulation/Delaunay, and hexagonal - each with its own character and its own reasons for existing. The move that makes any of them parametric is that the pattern is generated from inputs (a point count, a set of seeds, a surface) rather than drawn, so it re-solves when those inputs change. Master a handful of these and you can panelize almost anything.

The Voronoi diagram is the pattern behind cracked earth, giraffe hide, soap bubbles and a thousand "organic" facades. Given a set of seed points, it partitions the plane so that every cell is the region closest to one seed - each seed gets exactly the territory nearer to it than to any other. In Grasshopper the Voronoi component takes your points (and a bounding region) and returns the cells directly. Scatter the seeds evenly for a calm, cellular texture; cluster them with an attractor and the cells shrink where seeds crowd - which is exactly how you make a Voronoi screen densify around a focal point.

Its close relative is the Delaunay triangulation (the Delaunay Mesh / Triangulation components), which connects the seeds into triangles such that no seed lies inside any triangle's circumcircle - producing the "best-shaped", least-slivery triangles for a given point set. Voronoi and Delaunay are duals: they are two readings of the same seed points, and you can convert between them. Triangulation matters enormously for fabrication because every triangle is planar - three points always define a flat plane - so a triangulated skin can be built from flat panels even on a wildly curved surface. That single fact is why so many complex glass roofs are triangulated.

Both are driven by their seeds, so the whole game is in where you put the points - even, random, attractor-clustered, or noise-perturbed. The pattern is only as good as its point distribution.

This is worth dwelling on because it is where beginners lose control. If a Voronoi looks chaotic, the fix is almost never in the Voronoi component - it is in the seeds. Use Populate 2D for a uniform-random scatter (seeded, so it is reproducible), a jittered grid for a calmer regularity, or an attractor-biased distribution when you want the cells to tell a story. Master the seeds and you master the pattern; treat the Voronoi node as the last, dumb step that simply draws whatever your point logic decided.

Hexagonal tilings sit between the order of a grid and the softness of Voronoi. Hexagons pack the plane efficiently with only three panels meeting at each vertex (versus four in a grid), they distribute stress evenly, and they read as natural without looking random - which is why they turn up everywhere from honeycomb screens to the Eden Project's domes. You can build them from a hex-grid rule, but in practice most designers reach for a plugin.

LunchBox (a free, near-universal Grasshopper add-on) is the workhorse here. Its panelling components take a surface and return ready-made quad, triangle, diamond, hexagon and Voronoi panels mapped cleanly across the UV of the surface, plus staggered and diagrid variants - saving you from wiring the tiling logic by hand every time. For quick, robust panelization on a NURBS surface, LunchBox is usually the fastest honest route, and it plays well with attractors: panel the surface, then drive each panel's aperture or depth by distance or field.

A note on recursion, the other source of pattern: some systems are generated by repeating a rule on their own output - subdivide a triangle into smaller triangles, then subdivide those, and so on. True recursion in vanilla Grasshopper needs a loop plugin (Anemone or Hoopsnake) or a little scripting, because the standard canvas does not loop. Fractal and substitution tilings live here, but for most facade work a single-level tiling with attractor-driven variation gives you most of the richness with far less complexity.

A uniform tiling is just a mesh. The whole point of doing this parametrically is to lay variation over the pattern - and this is where Module 5 comes together. Once a surface is tiled, each cell has a centre (or a set of corners) you can measure and manipulate. Feed those centres into the attractor pipeline from lesson 5.1 and each cell's aperture, depth, rotation or infill responds to distance. Feed them into a field from lesson 5.2 and the variation flows smoothly and directionally. Feed them into noise (lesson 5.4) and the variation looks organic rather than mechanical.

Concretely: take a hex grid, get each hexagon's centre, measure distance to an attractor at the entrance, remap that to an offset amount, and inset each hexagon by its own value - now you have a screen that opens up around the door and tightens away from it, built from one clean rule. Swap the offset for a Z-extrusion and the same logic gives a relief of varying depth. Swap the attractor for a merged field and the opening follows a gradient. The tiling supplies the units; the attractor, field or noise supplies the story.

This composability is the real lesson of Module 5. Patterns, attractors, fields and noise are not four separate tricks - they are layers you stack. A tiling to divide, a field to modulate, a touch of noise to loosen it: that recipe, in various guises, is behind an enormous share of the parametric facades you admire.

With several tilings available, how do you choose? Ask three questions. What must the panels be made of? Flat glass or metal wants triangulation (guaranteed planar) or a grid you keep planar; a Voronoi of curved-edge panels is beautiful in render and expensive in reality. What is the surface curvature? A flat or single-curved wall tolerates almost any tiling; a doubly-curved surface pushes you hard toward triangles or carefully rationalised quads. What character do you want? Grid reads ordered and calm, hexagons natural and efficient, Voronoi organic and cellular, Delaunay crystalline.

Then build with fabrication in mind from the start. Keep each cell's data - its centre, its corners, its normal - flowing through your definition so you can later extract cut lines, label panels, and check planarity (LunchBox and Kangaroo both offer planarization help). A pattern that looks stunning but produces a thousand unique, non-planar, unlabelled panels is not a design - it is a problem handed to a fabricator. We treat rationalization properly in Module 6; here, just build the habit of asking "could this actually be made?" while the pattern is still on screen.

Get this right and tiling becomes the quiet backbone of your parametric work: a deliberate division of the surface that gives every later move - every attractor, field and grain of noise - clean, buildable units to act on.