In March 2022 I was contacted by a person named Glagolj who has mathematically described what I’ve been calling “wheel-within-a-wheel” designs made with Wild Gears.

He prefers to call it “second order roulette” as it involves rolling one curve on top of another curve. Fair enough. For me, a mystery. For Glagolj, a mystery to be figured out and encapsulated in a parametric equation.

He wanted to use the patterns I’d drawn by hand and compare them side by side with the renderings generated by his javascript plotter. That’s the ultimate check on the formula. As you can see here, it works.

The plotter can be found here. It allows you to plug in the four gear numbers of a second order roulette, and generate the pattern they should give.

Glagolj’s article on the formula is here on Github.

He prepared a couple of slideshows with some of the interesting patterns he found. These are all computer-generated, so he can use any gear he wants. Of course, working with physical gears we have to work with the ones we have. But the numbers are in the upper-left if you want to try drawing them yourself.

Here is the second slideshow by Glagolj:

Several people have suggested I try third-order roulette patterns, i.e. a wheel-within-a-wheel-within-a-wheel. Well, Glagolj is ahead of me there. Now I have to try to see if I can duplicate his computer-generated results.

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Inside a 120-tooth ring, I used a gear with 96 teeth, which has an off-center hole with 40 teeth. (I don’t remember which set this came from.)

Then I drew the pattern six times with six different small gears inside the 40 ring to see the patterns.

Looking at the math of it

Each time I got a 5-lobed pattern. That’s the basic geometry of the 120-96 gear combination, 5 loops or points, as you can see in the table here.

But there’s a lot of variation in how that 5-lobed pattern is expressed, according to which small gear is used.

Small gears used are: 32 (navy blue ink), 26 (pink). 34 (purple), 18 (green), 30 (red), 16 (turquoise).

Using the same table, looking at the number of points each gear would give in a 40-tooth ring, we see that:

• Gears 18, 26 and 34 all give 20 points
• Gears 32 and 16 give 5 points
• Gear 30 gives 4 points.

Now the differences in pattern density make sense. The three 20 point patterns (pink, purple and green) look different depending on the physical size of the gear.

The other three looser patterns make more sense if you try to count the points or loops within each lobe. Some of the points are hidden in the inner part of the pattern, so they’re hard to make out. But they’re there. You may get an idea from watching the video.

So the overall geometry of a wheel-within-a-wheel pattern depends on the larger gear/ring pair, and the density depends on the inner, smaller gear/ring pair.

Here’s the video, filmed on a sunny summer day in direct sunlight. The glass-topped patio table gives a nice flat surface for this work.

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There’s a link at the bottom to download it as a PDF if you prefer.

The post Super Spirograph 1969 Instruction Book appeared first on SpiroGraphicArt.

So, here are a bunch of different Spirograph patterns with instructions, plus some mystery patterns with no pictures! Follow the instructions and see them unfold.

The post 1967 Spirograph Refill Kit Patterns appeared first on SpiroGraphicArt.

A good toy store may carry the new Spirograph sets made by Kahootz. You can also find them on Amazon. There are many different sets available now, so decide what you want.

All links are affiliate links, meaning I may get a small commission if you buy something.

The most complete set is the Super Spirograph.

There’s also the regular (non-super) Spirograph deluxe set:

Some of the new sets have come with artwork borrowed by the old sets from the 1970s. Don’t be fooled; these are newly manufactured.

Kahootz also uses words like “Original Spirograph” to describe its product. This isn’t wrong at all, as the design is more or less the same as those made in the 1970s. The pieces are compatible, and the sets are mostly the same.

But the new sets are newly manufactured in China, and the injection moulding processes and materials used are not quite as good as they were back in the day. The pieces bend a bit and they are built with less precision in hole placement. The old ones were made in the UK, Canada, the US and perhaps elsewhere (if you know, please tell me in the comments).

There are even cheaper knockoff versions findable online, often pared down to a small number of components. I have not tried any of these sets.

Buying vintage

Real vintage Spirograph sets are better quality. You can look for them on eBay and Etsy. They often have a few pieces missing.

If you don’t live in the US, use eBay for your country or a country near you and search for “vintage spirograph”. For example, if you live in Portugal, try eBay.es (the Spanish version). Today when I search Spanish eBay.es for “vintage spirograph”, I see several sets available, mostly from the UK, but a few from France or Germany. There are also spare parts available if you’re missing a few pieces.

Do not worry about the pens! The old pens will have dried out anyway, and they really weren’t very good. There are so many great pens available now that work much better than the old pens and come in more and better colours.

Do not worry about the pins or the pieces of corrugated cardboard that came with the old sets. They aren’t necessary. If you do want to use pins, you can cut up an old cardboard box, or even better, use a cork bulletin board. But you don’t have to use pins. You can get poster putty, which is exactly the same as the “Spiro Putty” sold with the new sets, for a dollar or two at any office supply store. Blu Tack works too.

If you really want to buy the right pins, look for “map pins“. They are short and stubby, and will hold the ring to the paper properly.

Do not worry about the paper! You can use any paper. I usually use cheap photocopy paper for playing around. But when I want to make something nice, I use fancy paper, card stock, or even watercolour paper that I’ve sponge-painted.

Buying Wild Gears

Wild Gears is a different product. I’ve written a lot about it on this website. It is not compatible with Spirograph. It is much more expensive too, as it is not mass produced. But it’s fantastic. To purchase, go to WildGears.com.

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My favorite thing about this book is how it teaches you some basic principles about making Spirograph designs, then encourages you to improvise. Maybe, as it says, you can create a design that no one else has ever seen.

The writing style is relatively literary, compared to the minimalist writing found today. The booklet walks you through the different things you can do with one ring and one wheel, and takes you to the most difficult designs using two racks.

The older sets had one particular property that got lost sometime in sets made in the 1980s and later. The alignment mark was halfway up one side of the tooth. If you turned a wheel over and drew the same pattern again, it wouldn’t line up exactly. But this could be used to make a denser pattern. This feature is described in the booklet, and some designs are shown that use this technique.

This set also came with some sheets of paper that were divided in squares for drawing your nicest designs. The rings had lines that aligned with the squares, as you can see in the diagrams in the booklet. You could easily use them to make patterns with both rings, aligning them carefully with the squared paper.

Denys Fisher, by the way, was the inventor of Spirograph, and vintage UK sets carried his name. Sets made in the US and Canada did not, nor do the modern sets made by Kahootz Toys.

Thanks Ron, from all of us, for sending these photos and your observations!

Click on an image to see the slideshow of all the pages in the booklet.

The post Vintage Spirograph Booklet from 1968 appeared first on SpiroGraphicArt.

Are you missing a Spirograph wheel or gear? Did a key piece get broken? Did you buy an old second-hand set that’s short a few pieces? Are you wishing for more Super Spirograph parts to make different shapes?

Kahootz Toys, the makers of the new Spirograph, have set up a shop where you can order single Spirograph replacement parts.

Screenshot from Kahootz Toy’s former shop on Shopify, no longer operating.

The post Order Spirograph Replacement Pieces appeared first on SpiroGraphicArt.

EDIT: Aug. 13: See the bottom of this post for an update!

I (re-)discovered spirograph the 25th of June this year when I bought the starter pack with one ring and six wheels. The set was exactly the price of a pack of cigarettes in the Netherlands. I gave up smoking that day, successfully, and am very much involved in spirograph.

I have meanwhile gathered a collection of spirograph sets with the money I would have otherwise spend on smoking. Amongst them one from 1972 with a swing arm. Regretfully without the instructions, and I am very curious on how to use that piece. I have to admit I can not figure it out myself.

My question would be if you can help me out, or otherwise ask the visitors of spirographicart to clarify the “mystery”.

The mystery piece, labelled “SWING MARKER”

Note that the mystery piece has no teeth!

The only clue I see is on the cover of the box. It says ‘New “swinging action” designs!’ next to an unusual pattern:

Obviously this is a piece that didn’t make it to the next edition of Spirograph. If anyone has a booklet for this set, or can imagine how to use the toothless mystery “swing marker” piece to produce the design above, please let us know in the comments!

Here are the box cover and the rest of the set.

Apparently Spirograph can help you give up smoking! Congratulations, Ron!

EDIT August 13:

After looking at a photo referenced from a comment below, I had a “Eureka” moment about how it works.  You don’t need a swing marker, folks, unless you want reproducible results and recipes to follow.  I’m more of a slap-dash experimenter, myself.

It’s all about drawing a pattern while the ring is attached with only one pin (can’t do this with putty) and swinging between stops you’ve set with other pins. Bizarre, yes.

I’ll make a video when I get a chance (not for a couple of days at least). Meanwhile, I’ll share a picture of my initial experiments:

First try swinging spirograph.

Some totally different designs can be obtained.

Note that I’m using a corkboard here as a working surface to stick the pins in, as I described in one of my very first posts on this blog, before the new Spirograph or Wild Gears came out. I can imagine the pivot pin will wiggle itself out in time, probably more quickly if you’re using a corrugated cardboard backing.

Video coming in a few days. Meanwhile, give it a try!

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Conclusion: Spirograph is fun, but it’s a toy. Wild Gears is more expensive, and somewhat more difficult to use, but it’s a more serious drawing tool.

Shop Wild Gears at this link.

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Thanks for the great ideas! I’ve gone a more rudimentary, unwieldy, and not-so-artistic route but am mostly satisfied with it, though it’s a bit unwieldy.

I’ve used one of the cardboard boxes the Wild Gears ship in and used putty to adhere the gears to the inside of the box, arranged by size and labeled. I can fit the Full, Compact, and Strange Shapes gear sets on the large panel of the box and one of the two side flaps (except for the large gear set frames).

I like to be able to see everything at a glance, particularly when creating designs using a wheel within a wheel. That way I can see the size of the gear cutouts within the larger wheels. Keep the good ideas coming!

Shop Wild Gears at this link.

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