# What can one do with randomly generated parameterized knots in 3 space?

I have a way of generating random parameterized maps from $S^1 \to \mathbb{R}^3$. This method can create very simple knots, such as ellipses, but can also create knots with more crossings than I can count. The images can be knotted as I have seen the method generate a figure eight knot. I know that with a parameterization instead of a diagram one can compute things such as various knot energies. My question is the following: Is having the ability to generate random parameterized knots of use to anyone?

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Not a comment on the question itself but on the peculiar invented word you used: "parameterize". Statisticians talk about "parametric statistics", not "parameteric". But dictionaries don't help with the spelling. The usual pronunciation of "parametrization" is similar to "metrization". No one writes "meterization". (My credentials? I'm the founder but so far only member of the Foundation to Stamp Out Indeterminants.) –  Jim Humphreys Jul 16 '10 at 21:58
A computationally efficient method that finds lots of interesting knots could conceivably be folded into something like SnapPea, as a way to generate knots to test invariants against and measure run times, etc. In any case, this post reads as much like an advertisement as many I've read on MO. –  Theo Johnson-Freyd Jul 16 '10 at 22:20
Jim, I pronounce it "parameterization," with a stress on the am, though I swallow the syllable in "paramet(e)rize." I think that the difference is that I see metrization as moving to the metric system, not moving to the meter. Similarly, symmetrization comes from symmetric and geometrization comes from geometric or geometry. Perhaps we can compromise with "parametry" in place of -ization? (ps, no relation) –  Ben Wieland Jul 16 '10 at 22:32