Some time around 1968, when we lived in England, we got a Spirograph set for Christmas. It seemed a strange gift. The box was intimidating and adult – more like a drafting set than a toy. The cover showed a businessman working with the system, while his wife and children looked on in admiration and delight. Fun for the whole family, although only dad can touch it.

It become more interesting once we kids started to play with it. I needed help setting up the paper – it had to be fastened to a cardboard backing with push pins, then more pins were needed to hold a toothed ring in place, but then I started moving the gear around the ring, and it became an interesting challenge. The first problem was learning how to move the pen without sending the gear sliding away from its teeth and out of control. This could be infuriating. One slip and the wheel would go skidding across the sheet, ruining the pattern.

The set came with a tiny container of push-pins for mounting the plastic pieces onto the cardboard base. Once the cardboard had acquired enough holes, it became hard to get a good fit, and the plastic pieces tended to slip. I don’t think the set came with enough pins to account for the inevitable losses. You needed four to hold the paper down, and another four to hold the ring in place, so if you lost a few, the set became unusable until a passing baby found a missing pin with its knee.

Modern sets have done away with push-pins and use sticky putty instead. I’ve often wondered why the ring isn’t mounted on an arm that can swing down flat onto the paper. It would keep things much more stable. Too expensive, perhaps?

The pens were also a problem – the set included ballpoint pens in four colours – black, red, green and blue. Their tips were unusually narrow for the time. Because the set was designed around these pens, you couldn’t substitute a regular ballpoint pen – the standard Biro was too wide to fit. . Other Bic pens were narrow enough to fit the hole, but the tip was too short to reach through the plastic piece. Once the pens ran out – or if a sister had taken them to draw a four-colour horse – you were stuck.

Modern sets use wider holes for the pens, although it’s also much easier these days to buy a variety of ultra-fine pens.

Some combinations of ring and gear produced dull, simple patterns which repeated after just a few revolutions, while others produced more complex patterns that might take dozens of revolutions to complete. That was a part of the fun – you never knew what sort of pattern would appear, although, over time, I started to remember the combinations I liked. The best ones were those with the most ink around the holes.

The enclosed booklet included a gallery of possible patterns, in colour, and the instructions to create them. Many are a bit of a cheat – you draw a bit of a pattern, then shift the gears by 10 teeth and draw another bit.

For me, the holy grail was the one on the top row, second from the left – a circular pattern in red, green and blue, using the 150/105 ring and and the 52 gear. (The numbers referred to the number of teeth on each gear.) It’s a continuous pattern – no nasty jumping of teeth required, although you did need to change pens after each 18 loops. The sharp angles made it hard to complete without slipping.

Obviously I wasn’t the only one drawn to this design, as the same pattern has featured on the covers of many most Spirograph sets since the 1960s.

There were other, even more complex patterns, but most were impossible for my hands and stayed forever out of reach.

The old box cover also showed an owl drawn mostly from a series of Spirograph patterns. I don’t remember ever trying anything like this, or feeling any urge to. The pleasure of it was creating abstract patterns. Making Spirograph owls is Just Wrong.

Spirograph was invented by Denys Fisher, a British engineer who produced cannon parts for NATO. When not crafting weapons of destruction to annihilate the Red Menace, he played with automatic drawing machines, and made some devices from Meccano, the classic British building set.

If he were doing it today, he’d be more likely to use Lego Technik, like the guy in this video. The video shows the basic ideas well. A set of arms creates a shape. A turntable advances the drawing at a certain rate.

These kinds of drawing machines have been around for a long time. They were usually big, heavy, tabletop devices. Designs from the 1800s were used to create the complex patterns of lines used on banknotes. A repeating pattern might gradually change in size while the paper is slowly shifted. There had also been previous toys based on this kind of design, with a moving arm and a turntable.

Denys Fisher came up with the idea of turning a set of gears into a toy. The use of gears (rather than, say, moving arms with wheels and pulleys) meant that each pattern would come neatly back to its starting point. The product was an immediate success and won awards. Spirograph was quickly licensed to Kenner in the United States. The North American editions boot the businessman dad from the box cover and show kids having the fun.

Even people who have been turned off mathematics still find the graceful shapes of Spirograph pleasant and relaxing to work with. It shows how people can enjoy patterns that are strongly mathematical.

Modern sets don’t seem to have the same pieces as the set I had as a kid. The original set had 18 wheels, two rings, and two racks. Most newer sets drop a few of the wheels, or one of the racks, The current “original” set has only 15 wheels, two rings and and one rack, although it adds a few odd-shaped pieces. The “Super” Spirograph (now made by Kahootz Toys) is the cheapest set that has all the pieces in the original, the odd-shaped new pieces, as well as a set of snap-together customizable track pieces. It’s a fairly expensive set, so it’s probably better to stick with the basic version and put up with a few missing pieces.

I figured there must be computer versions of Spirograph, and, of course, there are. One nice interactive version, modelled on Spirograph, is Inspirograph. The developer worked hard to give it an organic feel and avoided what must have been a strong temptation to control everything with number menus and sliders. You can use a mouse to roll the wheel around, or press cursor keys to move it semi-automatically. I like the fact that, if you start to go over a line a second time, it actually produces a heavier line, just like in the real thing.

Another interesting development is WildGears, which began as a Kickstarter project making more sophisticated Spirograph-like rings and gears. They allow larger patterns, and a much wider array of types and sizes. The kits are laser-cut from a sheet of acrylic. They’re more expensive than Spirograph starting at $40 for an extensive starter set, up to nearly $800 for the complete, enormous range. At those prices, this is something the old-fashioned businessman dads will use while their adoring families look on in admiration.