3D Swimming Fish Algorithm

[Elroy]

Ok, this is an interesting one I'm working on.

I need to put together an algorithm that plots a random 3D path that looks something like what a fish's path would be in a fish tank.

I suppose another way to think of it is a screen-saver-type balls that moves around on the screen but always curves before hitting the sides. It would also get larger-and-smaller to simulate the third-axis.

In all cases, its range would be a bounded cube of arbitrary dimensions. I'd also like to control speed, but it could be relatively constant for any particular run. I'll think more about velocity once I get something up and running.

It'd just be a perpetual path.

Initially, I've thought of looking at some of the functions for French curves, or possibly adapting a Bézier curve, but I'm open to ideas.

I don't have any need to follow any particular function or algorithm, so long as it's a nice looking function. However, it will need to have a random component to it.

I'll keep exploring options, but suggestions are welcome.

Initially, I'll probably mock it up as a dot in a scaled picturebox.

Best Regards,
Elroy

p.s. I know this may more belong in a math forum than here. But I know y'all better than I know any of those guys. And I also suspect some great ideas will be provided here. Also, they'll also be more in code form rather than pure math algorithms.