this post was submitted on 24 Jul 2025
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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.