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Spirograph

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63 pointspeter_d_sherman17 comments

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Here are some interesting-looking Spirograph videos:

Spirograph Designs Compilation:

https://www.youtube.com/watch?v=39vZEvUBeSs

Wild Gears: Triangle Gear 120 in Ring 210 with Birdsong

https://www.youtube.com/watch?v=eC9dGWEc10Q

PDS: Speculation:

There is a relationship between the Spirograph toy -- and Fourier Series:

"But what is a Fourier series? From heat flow to circle drawings (3Blue1Brown)":

https://www.youtube.com/watch?v=r6sGWTCMz2k

PDS: Also, if I were to go for "full crackpot" (which I will, because I usually do! <g>) -- I'd speculate that fields, such as atomic, and subatomic fields (all particles -- because particles are basically all fields which act as particles) are "Spirographic"/Fourier Series in nature...

Yeah, I know...

"You're a crackpot!"

<g>

(Oh, an even more crackpot conjecture... I'd bet you could derive all of the quantum particles... from Spirographic designs/Fourier Series...)

The Wild Gears sets ( https://www.wildgears.com ) have enticed me a few time... though so far, I've been able to hold off on buying them for myself.

You’re a crackpot! What is an atomic field? Are you referring to the electromagnetic fields generated by subatomic and ionic particles? If so, they are indeed a linear superposition, whose constituents do have wavefunctions, which do include (spherical) harmonics.

AFAIK, no such thing as a particle as traditionally discussed exists at the subatomic level. A ‘particle’ is really a quantum excitation of the appropriate field. At least that is how we learned it in particle physics using current field theory and Feynman diagrams

If curious, past threads:

Drawing Spirograph curves in Python - https://news.ycombinator.com/item?id=17883187 - Aug 2018 (10 comments)

Spirograph Simulator (2014) - https://news.ycombinator.com/item?id=13256222 - Dec 2016 (40 comments)

Spirograph drawing - https://news.ycombinator.com/item?id=11026525 - Feb 2016 (1 comment)

Spirograph: Circles on circles rotating in opposite directions - https://news.ycombinator.com/item?id=6959404 - Dec 2013 (1 comment)

Spirograph in HTML 5 - https://news.ycombinator.com/item?id=5505467 - April 2013 (20 comments)

The mathematics of spirograph art - https://news.ycombinator.com/item?id=3777536 - March 2012 (2 comments)

I had one of these when I was younger, it was a lot of fun. Then someone got the bright idea to stick play-doh in the gears, and the fun diminished significantly.

As a math teacher, I love these things.

In a calculus class, I once gave a demonstration and then derived the parametric equations on the board.

In an introductory number theory class, I tasked my students with figuring out how to predict how many points a figure would have before drawing it.

I had a friend growing up who would give a Spirograph as a gift every birthday he went to for YEARS... not sure what the deal was, probably his mom just had it as the go to gift but forgot who he already gave it to.

I ended up with like three of them. They were fun, but I don’t think I needed three.

No more pins in the new versions. I played with them in the late 60s. We had pins.

This was one of my favorite toys as a kid.

The coolest digital spirograph images I've seen are from here:

https://spiromaniac.tumblr.com/

As a side note, I've been playing around with interesting mathematical functions like this as fun, visual coding projects. I had discovered the Lissajous curves[1], but I was curious if anyone else had any functions of this sort that are visually pleasing.

[1]https://en.wikipedia.org/wiki/Lissajous_curve

Ha ha, Lissajous curves.

I first discovered them in a math book, early on, in a phase when I had a craze for computer graphics programming. Plotted conics, sine and cosine, Lissajous, derived curves of all kinds, independently discovered an algorithm to draw Spirograph-like curves, etc. Some Lissajous figures I drew looked like yellow flickering flames. Good fun.

Edit:

Re: flickering flames:

Just looked it up:

"Rational ratios produce closed (connected) or "still" figures, while irrational ratios produce figures that appear to rotate."

From:

https://en.m.wikipedia.org/wiki/Lissajous_curve

Years later I blogged this:

Lissajous hippo, retrocomputing and the IBM PC Jr.:

https://jugad2.blogspot.com/2012/09/lissajous-hippo.html?m=0

I could never make it look like the pictures in the sample book - my excuse was that I was five years old. I did get kind of close once though.

Reminds me of general relativity because of the advancement of the perihelion of Mercury.

Ptolemaic propaganda I say!

Did you know that there's a direct correlation between the decline of Spirograph and the rise in gang activity? Think about it.

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