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Pick a math function, plot it in a circle instead of a line.
Also, plot something on a 2d plot then "crop" it with a circle. Crop circle. 
Algorithm you say? Moonshine + a brisk walk through a corn field should do just fine

This makes me want to plot a sine in a circle that matches up correctly for a full revolution. Is this some kind of circular harmonic? It has to be based upon PI somehow. This is going to bug me...

Damn you @skyjoe66! Now I am thinking a feedback loop that calculates the phase error after a full revolution. So I will pick the distance from origin. The phase feedback will adjust the frequency until the phase error is below a certain discernible amount.

skyjoe661655y@Demolishun or you could adjust the ratio between the function and where it's plotted on the circumference until a certain threshold is met. Or depending on the function you can search for a local minimum

@Demolishun I'm not sure what you mean, but you can parametrize a circle in R^2 cartesian coordinates like so
C := {(x, y) in R^2 such that [x = r sin(t), y = r cos(t), where r in R+ and t in [0, 2 Pi[}.
Gosh I hate not having latex on my phone 
pipe3275yMaybe not exactly what you want, but you could look into Apollonian Gaskets, aka circle within circles. That'd be a start!
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Does anyone know any algorithms for generating crop circles?
I would Google it but "crop circle codes" doesn't exactly give me what i want.
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