How can a Lissajous Curve be represented in 3D?

[tejolson]

I'm trying to figure out how to do a Lissajous Curve in 3d. It has a 2d shape in the real world, so if it's in the real world, then there must be a 3d shape to it.

Here is the crazy version, it has 8 variants of the last pic layered and it's at 45 45 0

This is the one above and it is at 0 0 0

Here is my version of that Lissajous by itself.

There are a million different ways to make pretty shapes out of that curve, but I'm pretty sure there is only one way it can be represented in 3d if it is to represent a real world example.

 

[phinds]

It has a 2d shape in the real world, so if it's in the real world, then there must be a 3d shape to it.

Why? Do you not believe in flat things? Yes, in the real world even a piece of thin paper has some thickness, so technically you are right, but I think you are carrying the concept to a point where it does not helpfully go.

... but I'm pretty sure there is only one way it can be represented in 3d if it is to represent a real world example.

Why? Why should it have ANY 3D representation?

 

[tejolson]

You're talking about a math function, I'm talking about something real. It is made with light. Some guy used two mirrors to make it. It's in 2d because it was viewed in 2d as it reflected off the wall. As I understand it there is a way to slow down light in a vacuum. Maybe I can see a 3d representation that way. But I'm thinking it won't work because a photon is to small to see?

It's a wave function that uses binomial distribution. From what I understand quantum physics uses probability, and binomial distribution is part of probability. So I'm thinking there is a connection and I want to understand it.

 

[tejolson]

Yup, I'm right. Apparently there was an experiment done a long long time ago. A professor told me the 3d version of the x,z or y,z plane is itself a Lissajous figure. So that makes those figures above correct. Unfortunately this means this stuff is already known. And since it's already known then it's been done and it does not need to be redone. If anyone knows who did this experiment in 3D, I would very much like to know. The professor that talked to me was unsure about the details.