Need an asymetric curve

This is for an art project, hence Cafe Society. It ried fractals, too busy. Tried logrhythmic, too swirly. What I need is a nice smooth curve that starts one way and then goes the other, but not as regular as a sine wave. Sort of French Curve-ish, but just one, not a bunch of 'em.

Dimensions are 16" long by 6" wide, to be specific.

What are you actually looking for? An equation? A physical object? A pointer to something you can buy? Just ideas?

A picture of the curve would be excellent. I’m going to be putting organ pipes along the curve, so if it had nicely spaced dots, each a bit further than the previous, that would be even awesomer.

Here’s the log curve I tried first. That works great except for being mostly square rather than rectangular. I tried stretching it but didn’t get anything I liked.

Have you looked through Google images of French curves? Also look at ship’s curves and Vary Form curves. If you are getting a physical product, look at flexible curves; they let you make whatever form you want and are marked like rulers.

Illustrator and beziers are your friends.

Don’t know what you want exactly, but have a look at these:

Power curves greater than parabolas (y = x[sup]n[/sup], where n > 2). For odd powers, the curves start low and go high.

Exponentials and Logarithms


Super Ellipses

Trigonometric functions and inverse trig functions. You mention sines, but have a look at tangents, for instance, and inverse tangents





Lorentzian (Witch of Agnesi)


Hyperbolic Cosine

Pursuit Curves

y = x³?

If the OP was trolling, I’d suggest a Poisson distribution.

I have only the faintest idea what you are seeking, but I’d like to suggest you try tracing along the side of some of these things:




Old Coca-Cola bottle

Thistle flower