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? ಠ_ಠ
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.
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.
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
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? ಠ_ಠ
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.
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.
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