Understanding tilings

Have a look around you, what do you see? Maybe a tiled bathroom wall, a brick facade outside the window, maybe a honeycomb-patterned scarf. You've been surrounded by tilings your whole life, but you may never have used that word for them.

A tiling covers a surface with repeating shapes, leaving no gaps and no overlaps. People have been playing around with this for a very long time: think back to the Persian and Moorish tilework we admired in Module 1. Those craftspeople were working out, by hand, the same geometry you're about to harness using Repper.

A tiling is like a recipe for how to make a pattern. If you imagine your sample selection the ingredient, the tiling is the set of instructions that repeats it across the surface.

Alexander, the technical brain behind Repper, explains it in more detail:

The same ingredients with a different recipe means a totally different dish. The same is true for patterns! Using a different tiling and you get a totally different pattern:

So what's inside such a recipe? Surprisingly little. Every tiling is built from some combination of just three moves:

There's technically a fourth called the glide: a reflection and a move combined. Footprints in the sand are the classic example: left, right, left, each one a flipped and shifted copy of the last. We won't dwell on it, but now you can name it when you see it.

Tilings are made up of a series of instructions, from one up to dozens! Here you see an example of how the Bow Tie tiling in Repper is built up:

Don't worry if this dazzles your brain; it does mine to when I think about it :) All these recipes are built into Repper, so you don't need to understand them in detail. Repper does all this automatically, so you can focus on getting the look you're after. Because more than just build the pattern, these tilings determine its mood. Reflection create balance: a mirrored pattern feels calm and settled. Rotations create energy: things seem to spin, swirl, and dance. Once you start seeing patterns this way, you can't unsee it.

Here you see an example of the Echo Honeycomb in action, a tiling in Repper where you can even adjust the reflection in your pattern:

The three moves also explain the shape of your sample selection. Triangles, squares, hexagons: each tiling gives you the shape that fits its particular dance, which is why the selection changes when you switch tilings. The left example below has a straight reflections and therefore a rectangular sample, whereas the right one has two diagonal reflections as well, so the sample because a triangle instead. Have a look and see if you can make sense of it.

Open the tiling selector in Repper and you'll find 40 tilings. That can feel like a lot, but we can already simplify by looking at two big buckets: "seamless" and "seamed".

Seamless tilings repeat with visible seams (it's really in the name :-). They achieve this by relying entirely on reflections. Zoom out and you can't tell where one tile ends and the next begins, which is generally great for fabric, wallpaper, or anything printed edge to edge. On the other hand, seamed tilings use moves and rotates and thereby reveal hard edges.

So it's really down to reflections. When a tiling mirrors your sample along the tile edge, the two sides match perfectly and the seam disappears. No mirror at the edge, no match. Look back at the move/rotate/reflect image earlier in the article. Now you know why the first two have hard edges!

Some tilings are basically siblings, with the difference being one reflection to turns the tiling seamless. The Bloom and Circle Saw tilings are an example of this:

Another clear pattern (heh) you see when looking at the tilings, is that they range from simple to complex. Feed the same sample to Half-Brick and to Persian Star (one of my favorites) and while the first gives you a orderly repeat, the other erupts into intricate geometry. Neither is better. Complexity isn't something you need to level up to, but simply a dial you get to turn depending on the aesthetic you're after.

And a few tilings, like the Cairo you met in Module 2, come with their own extra controls, multiplying the possibilities from a single recipe.

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Now that you know the difference, you might be tempted to treat seamless as "good" and seamed as "broken". Please don't! Seamed tilings are a little harder to work with, but offer unique pattern possibilities.

Because of the way the seamed tilings are constructed, they bring energy and directionality. Textile designer Becka Rahn turned a dog illustration into a delightful novelty repeat using a seamed zigzag, and we agreed in our interview: seamed tilings reward the designers who dare to play with them.

Find the edges too harsh anyway? Some of the seamed tilings have an Edge Blend option that softens the joins. This video helps you on your way (Michel has a particularly smooth presentation in this one ☺️):

Before we wrap up, a quick taste of the exotic end of the map.

The Penrose tiling, first described by mathematician Roger Penrose in the 1970s, never exactly repeats. Zoom out as far as you like: while it looks self-similar, the structure is never quite the same. It's a fascinating and gorgeous pattern!

In this oldie-but-goldie video, I show you show the Penrose tiling works:

Here's where's we get to the big payoff of this whole big chapter. Tilings aren't boring geometry homework. Tilings are creative choices, like choosing a brush or an instrument. In one of our pattern contests, a winning collection was built entirely on the bold angles of the HighFive tiling, and the jury loved it precisely because that choice became the collection's signature.

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You now have a better vocabulary and way to reason about tilings: how are they built up, seamless or seamed, simple or complex, etc. In the next chapter, we'll zoom out from the geometry to the feel of a pattern as a whole: what gives it weight, balance, and togetherness. Time to find some harmony.