I want to set up an expression which generates a curve.  The curve (vaguely
remembered from 25yo materials science classes) should look like the diffusion
equation in one dimension, or perhaps a Poisson distribution.

The closest thing I can find to it on the web involves a factorial in the
denominator.  I'm pretty sure the actual diffusion equation doesn't have a X! in
the denominator, and I guess that povray cannot do X! for fractional values.
But what I want is a curve generally of the shape like so:

http://www.wolframalpha.com/input/?i=%28e^-6.3%29%2810^x%29%2Fx!+from+0+to+15

Looking for something f(0)=0,  with a single maximum at medium values, and very
slowly decays back to zero. The actual diffusion equation (as I remember from
long ago) would do that.  Like the smell on the opposite side of a room after
you open bottle. (Want it for my flocking formulas).

any tips?

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> http://www.wolframalpha.com/input/?i=%28e^-6.3%29%2810^x%29%2Fx!+from+0+to+15
>
> Looking for something f(0)=0,  with a single maximum at medium values, and very
> slowly decays back to zero. The actual diffusion equation (as I remember from
> long ago) would do that.  Like the smell on the opposite side of a room after
> you open bottle. (Want it for my flocking formulas).

If you're after something simple, how about x/(x^2+a^2) which will give 
you a peak at "a" and tail off slowly.

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scott <sco### [at] scottcom> wrote:
> > http://www.wolframalpha.com/input/?i=%28e^-6.3%29%2810^x%29%2Fx!+from+0+to+15
> >
> > Looking for something f(0)=0,  with a single maximum at medium values, and very
> > slowly decays back to zero. The actual diffusion equation (as I remember from
> > long ago) would do that.  Like the smell on the opposite side of a room after
> > you open bottle. (Want it for my flocking formulas).
>
> If you're after something simple, how about x/(x^2+a^2) which will give
> you a peak at "a" and tail off slowly.

great, thanks.

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