How to plot four variable vector-valued function in MATLAB?

Hi,

what module do I need to plot the four-variable vector-valued function such as

v(x, y, z, t) = (x*y*z*t)i + (x^2 − y^2)j + (3*z + t)k ?

or do I need to parametrize this equation in some-way to plot it? Can someone give me a clue to how to proceed?

Thanks.

Answer 1

[John D'Errico]

It is no problem. Well, at least not if you have a hyper-dimensional holographic monitor. (Mine is broken, and awaiting parts delivery.) Starfleet starts making them in the 23rd century or so. But then shipping is a problem, as only the Borg are willing to make deliveries. And do you really want the Borg showing up at your front door? I won't even get into the difficulties of mail orders into the future.

Seriously, you can't plot it. Your mind is not equipped to visualize stuff in more than 3 dimensions. Yes, you can understand stuff in 3-d. Even a picture of something in 3-d can be deceiving, as one should know by looking at any M.C. Escher print.

What you see on a computer monitor, or in any figure you can generate, is a 2-d projection of something that lives at most in 3-dimensions. Once you go beyond that, things get terribly confusing. (Try displaying a projection of a 5-dimensional hyper-cube in a figure.)

You have something that is a function of 4 variables. Essentially a vector that itself lives in 3 dimensions, as a function of 4 other variables. Essentially, you have a 7-dimensional process that you want to plot.

The good news is, maybe 7 of 9 will be making your delivery when the Borg show up.

[Saurav Parmar]

well...I am not even looking for multidimensional representation of the equation...am looking for a way how it can be represented in two dimensions?

[John D'Errico]

There really is no simple way to do so. I'm sorry.

Some people have chosen to use color to represent multiple dimensions. But color itself is only 3 dimensional, and even then it would be difficult to visualize what is happening. (How good are you at distinguishing colors, and from the color, infer the approximate RGB coordinates?) Worse, your problem is effectively 7 dimensional. So you might use things like the thickness of a line, or the size of a marker, in addition to the color. The result would be an unintelligable, meaningless mess.

Contact Starfleet, and wait for a reply.