High Quality: https://www.reddit.com/r/woahdude/comments/anh3os/lissajous_curve_table/#lightbox
Interactive: https://www.intmath.com/math-art-code/animated-lissajous-figures.php
Interactive 2: https://lissajous.space/
this post was submitted on 24 Jul 2025
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Jesus fuck this is fascinating.
I immediately went "oh f- I need to post this" when I discovered it.
this reminds me of this one:
it's from this youtube video. huge shoutout to 3blue1brown for their amazing videos about the fundamental principles and objects of math!
the video is very very watch-worthy, especially if you actually intend to understand something about very important math, though i'm not sure whether it's the first video in a series. it could be that it's based on another video by 3blue1brown, go check out their whole channel, in fact, it's amazing.
This is awesome, thank you.
Whatβs going on here exactly?
First horizontal and first vertical circles draw the rest (at different speeds)
tip: get high, and watch this while squinting
source: π
it's beautiful, i've looked at this for five hours now
If anyone finds something similar, PLEASE post it.
Wait... I can't (fully) wrap my head around how it is not symmetrical about the diagonal. I guess they're the same curve saw from different planes but... It doesn't seem to make sense? The pairs are in sync, but look like they aren't? ΰ² _ΰ²
Edit: whoa, guess this is also a great representation of harmony. Simple graphs are consonant intervals, complex ones are dissonant
It could, if you kept the speed but changed the starting point of one of the circles. The result would be getting gradually squished circles until you got a line.
This is technically called changing the phase.
The point (x(t),y(t)) is describes by (cos(nt),sin(mt)) were n,m = 1,2,3,... are the rows and columns respectively. It looks different across the diagonal because you have a phase difference, i.e. a different starting location
I was wondering this too, I think it's because:
If you look at the trace at the row1,col2 position it moves left and right twice as fast as it moves up and down, where as the row2,column1 trace moves up and down twice as fast as it moves left and right.
So they could never be identical, but maybe you would expect them to be rotated 90 degrees?
But that would fail too since they all start at the top center position, but if you rotate the "n" shaped trace it wouldn't touch the top center.
If you looks at the interactive link OP posted https://www.intmath.com/math-art-code/animated-lissajous-figures.php you can play with the phase shift which controls if you get an n or and 8 shape, or something in the middle.
Ah the joys of playing with an oscilloscope.
It's amazing how you can tell which numbers are prime just by staring at this.
I don't understand, what numbers are there to be prime or not? I see graphs and frequencies only.