You could also have a 3D spirograph where you rotate an object with an embedded "pen" around the inside of a sphere, say. It draws a 3D shape. This would be very hard to construct, but easy to simulate. Would it give you anything interesting, either as a line drawing or a surface?
I'm not sure, because you would have an additional degree of freedom that needs to be constrained. With a 2D spirograph, you only have one axis of rotation. You can rotate forwards or backwards, but there are no other options. With a 3D object, there are always two possible axes of rotation. The simplest way to handle it would be to only rotate around one axis, but then you are back to just a normal 2D spirograph. There would need to be some non-linear correlation between the rotations, which adds a great deal of complexity.
After seeing the Spinor 'belt' animations on that page, something in my gut is screaming at me that there's some great use for this phenomenon in EMF power generation.
"I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me."
This is nice. I wrote a spirograph simulator when I was 14 years old, but of course it didn't have such nice UI (basically it was just a couple of calls of sin(x) and cos(x) in a loop, and some graphics calls, it was much fun nonetheless).
Some ideas:
- Animate the rotation of the gears more smoothly for more realism.
- Add an automatic mode, where the gears keep on moving until it reaches the point when the path starts overlapping itself.
I like physical things and I liked the original Spirograph. But that simulator is so much easier, quicker, and more flexible. You can't even mess up by popping your pen or slipping gears.
Really, there's no reason to own a real Spirograph anymore. You might still want a Spirograph for the same reason you'd want a Curta or an Enigma, i.e., for nostalgia or as a collector's item or to behold the sheer coolness of it. But you or your kid would never play with a Spirograph today, or calculate with a Curta, or encrypt with an Enigma.
I say all this with a bit of sadness because I miss things that I could hold with my hand.
I completely disagree; kids learn a lot by using physical devices, that they won't learn from digital simulations. I think the best we can offer them is a mix of both.
Physical devices develop dexterity and attention to detail. For example, drawing a circle with a compass develops a number of physical abilities. Some kids love the challenge of making neat circles of different sizes, and they'll get something out of using a compass that they'll never get from a digital circle-making tool. And keep in mind, there are different kinds of compasses. There are the pointy-tipped kind that we all think of, and there are flat ruler-types that have a spinning pivot point. Someone who's used these kinds of devices can develop a very concrete understanding of what a radius and a diameter is, among other things. I believe some of the same benefits come from working with a physical spirograph.
Digital simulations allow people to try out many more variations in a short period of time than they could with a physical device. Digging into the code behind these simulations pushes people to understand the mathematical concepts that underlie these tools and patterns.
Our young people can have the best of both worlds; it's our job to help them enjoy the variety of tools that are available to them today.
>> your kid would never play with a Spirograph today
That just represents AFK parenting. If your 5-8 year old is being babysat by the television or iPad, it is hardly their fault that they aren't experiencing anything hands-on.
What always struck me as interesting is how some of them 'seem' like they're a projection of a surface onto the plane.
Edit: In fact, it would be nice to see a 3d version where the z-axis is the angle of incidence between gears (taking one as reference).
Especially in crazier patterns with gears that are not perfect circles. Too sad this is far in the past: https://www.kickstarter.com/projects/465068187/wild-gears-20...
Note: in the starting position when you open the page, fixed 96, rotating 52. 13 revolutions for the curve to close. 52=4x13=gcd(52,96)x13