One Single Line #tessellations

Amazing how simple a tessellation can be. One single line. Maybe a fill colour. Over the years I’ve amassed quite a few designs, some are copies of designs I have seen, some are my own creations, some are from the ancient art of Islamic Geometric design. Just blows me away.

Below, I will compare the technical grid of single lines and final design. Sometimes the structure is quite apparent, sometimes not. The grid of lines behind can be quite complex. The brightly coloured image on the left, shows the single line with its repeats in different hues, the image on the right, a complete design.

Louis Cubes defined by a single squared spiral element repeated on its different faces. Tap any of the images to get a larger view of it, and swipe to see the complete design:

The Islamic Geometric design know as the Damascus design, shields and stars — one single, short, strategically placed line, but with a tremendously complex grid behind it. Not an easy one to get perfect:

This tessellation is a modification of the Zentangle design called Cadent. It is usually based on four rotation points, but below, I have used 6 way rotation instead, the whole achieved with a single curve:

Simple Red Stars around a Black Hole, done in symmetry group P6m. Again, one single line for the whole design!

The Flower of Life design, older than the pyramids, found engraved on stone in the Middle East, and elsewhere around our planet. A complex grid behind a single simple arc.

Shattered glass shards, this is also a single line with a slight angle in it. The fill colours help to defined the concept. Symmetry group P6, a 6-way, a 3-way and a 2-way rotation point, with the line avoiding contact with any of these, simply dancing at the outer edges:

This Islamic design comes up frequently in the Alhambra. I recreated this one in symmetry group P6, a single arc from the 6-way rotation point. An absolute favourite:

Below, a simple Staircase design, one single zigzag line with a few angles thrown in.

Water droplets, des Goûtes. One apostrophe arc. That’s it. This one is built using symmetry group Pgg, two glide reflecting lines at ninety degrees with a two-way rotation point in the middle of the rectangle:

A few more Islamic Geometric designs, all built with a single line. Amazing artists. The complexity of simplicity. The first image is the Abd al-Samad design, and the second one is from the Mustansiriya Madrasa:

I-beam tessellation, was the first design I created that brought the concept of a single line as the basis for a complete nested shape. It is built using symmetry group P4g, around a 4-way rotation point, in the middle of a mirror box:

Aleppo is a recent discovery for me, again, from my study of Islamic Geometric designs. A bit more complex than the above lines with a single angle, as the line has many segments and four angles. Similar in mind to the children’s game of drawing an envelope with a single stroke, without lifting your pencil, without crossing lines or drawing on top of it again:

Cordage, rope work, this one also a strategically placed compound curve. Took me a while to get the correct spot to drop the line, much tweaking was required:

Starlike Labyrinth in P6. This one has six angles to it, built in a similar fashion as the Louis Cubes at the start of this discourse, but with a blank hexagon in the grid:

A simple Basket Weave, created with a single segment, no angles. This tessellation built using symmetry group P4g:

The last section in this “one line tessellations” series is a more complex and fluid-line design. My One-Line-Dude, requires a bit of imagination at the start to be able to see a figure inside the outline; but I have done all the line tweaking work for you to make it easy. The dot helps define the eyes. And of course, character features, clothing and colour also help:

Cheers! Hope you enjoyed this lengthy article.

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