We’re pattern-seeking creatures. Whether you put this down to evolutionary defensive instinct or a higher-sourced aesthetic appreciation, the fact is we can’t help seeing structure and repetition. This happens even where it doesn’t exist, as shown by lottery-playing numerologists. More positively, patterns play an important part in art in practically every culture and age. In 1943 Alfred Whitehead, an English philosopher and mathematician, said that “art is the imposing of a pattern on experience, and our aesthetic enjoyment is recognition of the pattern.” This holds true from the monumental architectural designs of ancient Greece (Doric, Ionic and Corinthian) to the personal decorative designs of Aboriginal tattoos, and of course in the visually and mathematically beautiful designs of Moorish and Islamic art.

I talked about patterns in camouflage in Dazzle and Digital Camouflage, but repeat patterns is another part of this area of design, and it is worth a closer look. Creating complex, detailed graphics that work across repeats can take time, but it is time well spent. The field of Surface Design in particular relies strongly on generating and manipulating repeating patterns, and the key techniques to practise for this kind of work are translation, reflection and rotation.

Here, translation isn’t anything to do with linguistics. In this discipline it means repeating by moving; in other words, sliding and copying. At the most basic, think of potato-stamp printing; anything that simply repeats a design over and over across a surface. Option-dragging does this in most applications, as do the better Duplicate commands. As a graphic manipulation operation this is fairly simple, but it can be highly effective. Create elements that straddle the adjacent sides of repeating design units and the edges of the actual repeats will start to be hidden in the array of design elements.

Reflection adds some spice to pattern generation recipes. Rather than simply replicating something and letting the elements inside the design units do all the work, the shapes are flipped, mirroring the core artwork along a line of symmetry, the reflection axis. This is found in a lot of classical designs, where symmetry and balance were held in high regard.

Finally, rotation simply defines a point relative to the original and rotates a copy around that point. If you’re using Illustrator click and drag with the Rotate tool, holding down the Option key to duplicate rather than just move the original. Use this tool to reposition the centre point first. In pattern generation rotation is often done stepped at some clean division of 360 degrees; 60° (for six steps around), 45° (for eight around), 36° (ten around), 30° (twelve around), 24° (fifteen), and so on. Other values are possible, although you’ll have to use decimal fractions to get things spaced evenly. Rotating a copy every 51.4285714285714° will give you seven instances in a circle – although to be honest you only really need a precision level of two decimals for most work. These three manipulation methods are quite simple, but with a little thought and practise – especially if mixed together – the results can be extraordinarily rich and complex.

Sophisticated pattern repeats are a core part of Islamic art, and one of the key motifs there is the star pattern – which is often, graphically speaking, a combination of rotation and translation. This is an ancient graphic development that reached a zenith 500 or so years ago and can be found as far apart as Spain and Morocco in the west and Uzbekistan and some other ‘stans in the east. This star pattern is a mathematically and geometrically based structure, but one of the curious things about these designs is that we know next to nothing about how the designs were actually developed; at least not much beyond what we can surmise through logic and applied geometry. The craftsmen and artists who produced the patterns considered the process to be secret knowledge, restricted information like the recipes for Coca-cola and KFC are today. We know the work is based on a thorough and widespread understanding of Euclidian planar geometry, and there are countless designs available to study, but we don’t know the specific detailed planning that went on behind the end results. If only they’d used design sketchbooks!

Fortunately, developing new forms based on these artworks is a great exercise in geometric explorative design. I’m not suggesting anything as crass as trying to recreate the intricacies of the work in Cairo’s Ibn Tulun Mosque in five minutes, but it is a useful way to develop some graphic insights and perhaps get some inspiration. To begin with, use Illustrator to draw a circle that is 100mm in diameter, with a plain 1pt stroke and no fill. Duplicate it and place the copy with its centre aligned on the first circle’s edge. Now create another copy of the circle and place the centre where the lines of the original and the previous copy cross. Repeat around the first circle until you have six arranged equally around the circumference. There are various ways of doing this, including using the Rotate tool with the point on the original’s centre and turning 60° each time.

Use the Pen tool to draw a path from one junction of circle paths to the next, and you’ll end up with a regular hexagon. Next, draw a path from the mid-point of one of the hexagon segments to the midpoint of the segment two sides around. In case that wasn’t clear, you’re aiming to have an equilateral triangle that sits with its points mid-way along lines of the hexagon. Duplicate and flip (i.e. rotate 180°) and slide it down to form a six-pointed star. Use the Pathfinder palette to unite the triangles into a six-pointed star. Give the hexagon a grey fill and fill the star with white; this will make it easier to see the structures as they form, and it will also help with selecting things later on.

Yes, we could have made these shapes in a slightly more direct method, but starting with circles, using them to build hexagons and then stars, and progressing through rotation and translation techniques – this is a good way to build up a strong feel for the geometric relationships and underlying structural base. Trust me.

Now select everything and, holding down the Option key, drag across and down to place the new hexagon against the old and line up points of the stars. With Snap To Point selected in the View menu it should line up relatively cleanly and easily in one go. Then choose Object > Transform Again. And again, and again. Once you have half a dozen or so instances, select everything, and Option-drag upward and across to align a copy of it all as before. Repeat the operation with Transform Again a few times and you’ll have a tessellated pattern covering part of your page and far into the pasteboard as well.

This is really a starting point, the stage where you can draw paths along routes through the design, slicing it up to get over and under effects, draw diamonds over the implied shapes made by the stars and hexagons, or whatever else takes your fancy. But first, select one of the circles and choose Select > Same > Appearance. Because only the circles have strokes but no fills, only those will be selected. Now you can move them safely to a new layer or delete them as you see fit.

How you develop this is entirely up to you and your creative urges. But do spend time researching the geometric developments of Islamic design, and then compare this to the illustrative genius of M. C. Escher. The pattern-generating possibilities of translation, rotation and reflection are endless.